@article {Linearized,
    AUTHOR = {Engl, Heinz W. and Kunisch, Karl and Neubauer, Andreas},
     TITLE = {Convergence rates for {T}ikhonov regularisation of nonlinear
              ill-posed problems},
   JOURNAL = {Inverse Problems},
    VOLUME = {5},
      YEAR = {1989},
    NUMBER = {4},
     PAGES = {523--540},
      ISSN = {0266-5611},
       URL = {http://stacks.iop.org/0266-5611/5/523},
}



@article {Multifrequency,
    AUTHOR = {Bao, Gang and Li, Peijun and Lin, Junshan and Triki, Faouzi},
     TITLE = {Inverse scattering problems with multi-frequencies},
   JOURNAL = {Inverse Problems},
    VOLUME = {31},
      YEAR = {2015},
    NUMBER = {9},
     PAGES = {093001, 21},
      ISSN = {0266-5611},
       DOI = {10.1088/0266-5611/31/9/093001},
       URL = {https://doi.org/10.1088/0266-5611/31/9/093001},
}
	


@book {EHN96,
    AUTHOR = {Engl, Heinz W. and Hanke, Martin and Neubauer, Andreas},
     TITLE = {Regularization of inverse problems},
    SERIES = {Mathematics and its Applications},
    VOLUME = {375},
 PUBLISHER = {Kluwer Academic Publishers Group, Dordrecht},
      YEAR = {1996},
      ISBN = {0-7923-4157-0},
}


@article {Tikhonov2,
    AUTHOR = {Tikhonov, A. N.},
     TITLE = {On the stability of inverse problems},
   JOURNAL = {C. R. (Doklady) Acad. Sci. URSS (N.S.)},
    VOLUME = {39},
      YEAR = {1943},
     PAGES = {176--179},
}


@book {Tikhonov,
    AUTHOR = {Tikhonov, Andrey N. and Arsenin, Vasiliy Y.},
     TITLE = {Solutions of ill-posed problems},
    SERIES = {Scripta Series in Mathematics},
      NOTE = {Translated from the Russian,
              Preface by translation editor Fritz John},
 PUBLISHER = {V. H. Winston \& Sons, Washington, D.C.; John Wiley \& Sons,
              New York-Toronto, Ont.-London},
      YEAR = {1977},
}


@article {JohnFritz2,
    AUTHOR = {John, Fritz},
     TITLE = {A note on ``improper'' problems in partial differential
              equations},
   JOURNAL = {Comm. Pure Appl. Math.},
    VOLUME = {8},
      YEAR = {1955},
     PAGES = {591--594},
      ISSN = {0010-3640},
       DOI = {10.1002/cpa.3160080409},
       URL = {https://doi.org/10.1002/cpa.3160080409},
}


@article {JohnFritz,
    AUTHOR = {John, Fritz},
     TITLE = {Continuous dependence on data for solutions of partial
              differential equations with a presribed bound},
   JOURNAL = {Comm. Pure Appl. Math.},
    VOLUME = {13},
      YEAR = {1960},
     PAGES = {551--585},
      ISSN = {0010-3640},
       DOI = {10.1002/cpa.3160130402},
       URL = {https://doi.org/10.1002/cpa.3160130402},
}



@article{hadamard,
	Author = {Hadamard, J.},
	Journal = {Princeton University Bulletin},
	Keywords = {ill-posed, problem},
	Pages = {49-52},
	Title = {Sur les probl\`{e}mes aux d\'{e}riv\'{e}s partielles et leur signification physique},
	Volume = {13},
	Year = {1902}
	}


@book {HadamardCauchy,
    AUTHOR = {Hadamard, Jacques},
     TITLE = {Lectures on {C}auchy's problem in linear partial differential
              equations},
 PUBLISHER = {Dover Publications, New York},
      YEAR = {1953},
}


@book{IntroLavrentiev,
	AUTHOR = {M. M. Lavrentiev},
	TITLE = {Some Improperly Posed Problems of Mathematical Physics},
	PUBLISHER = {Springer Berlin, Heidelberg},
    SERIES = {Springer Tracts in Natural Philosophy},
    VOLUME = {11},
      YEAR = {2013},
      ISBN = {978-3-642-88210-4},
      DOI = {https://doi.org/10.1007/978-3-642-88210-4},
}



@article {maxwellis,
    AUTHOR = {Isakov, Victor and Lai, Ru-Yu and Wang, Jenn-Nan},
     TITLE = {Increasing stability for the conductivity and attenuation
              coefficients},
   JOURNAL = {SIAM J. Math. Anal.},
    VOLUME = {48},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {569--594},
      ISSN = {0036-1410},
       DOI = {10.1137/15M1019052},
       URL = {https://doi.org/10.1137/15M1019052},
}



@article {Source3,
    AUTHOR = {Isakov, Victor and Wang, Jenn-Nan},
     TITLE = {Uniqueness and increasing stability in electromagnetic inverse
              source problems},
   JOURNAL = {J. Differential Equations},
    VOLUME = {283},
      YEAR = {2021},
     PAGES = {110--135},
      ISSN = {0022-0396},
       DOI = {10.1016/j.jde.2021.02.035},
       URL = {https://doi.org/10.1016/j.jde.2021.02.035},
}


@article {Source2,
    AUTHOR = {Entekhabi, Mozhgan and Isakov, Victor},
     TITLE = {Increasing stability in acoustic and elastic inverse source
              problems},
   JOURNAL = {SIAM J. Math. Anal.},
    VOLUME = {52},
      YEAR = {2020},
    NUMBER = {5},
     PAGES = {5232--5256},
      ISSN = {0036-1410},
       DOI = {10.1137/19M1279885},
       URL = {https://doi.org/10.1137/19M1279885},
}
		




@article {IK11,
    AUTHOR = {Isakov, Victor and Kindermann, Stefan},
     TITLE = {Subspaces of stability in the {C}auchy problem for the
              {H}elmholtz equation},
   JOURNAL = {Methods Appl. Anal.},
    VOLUME = {18},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {1--29},
      ISSN = {1073-2772},
       DOI = {10.4310/MAA.2011.v18.n1.a1},
       URL = {https://doi.org/10.4310/MAA.2011.v18.n1.a1},
}


@article {Evidence2,
    AUTHOR = {DeLillo, Thomas and Isakov, Victor and Valdivia, Nicolas and
              Wang, Lianju},
     TITLE = {The detection of surface vibrations from interior acoustical
              pressure},
   JOURNAL = {Inverse Problems},
    VOLUME = {19},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {507--524},
      ISSN = {0266-5611},
       DOI = {10.1088/0266-5611/19/3/302},
       URL = {https://doi.org/10.1088/0266-5611/19/3/302},
}


@article {Evidence1,
    AUTHOR = {Colton, David and Haddar, Houssem and Piana, Michele},
     TITLE = {The linear sampling method in inverse electromagnetic
              scattering theory},
   JOURNAL = {Inverse Problems},
      NOTE = {Special section on imaging},
    VOLUME = {19},
      YEAR = {2003},
    NUMBER = {6},
     PAGES = {S105--S137},
      ISSN = {0266-5611},
       DOI = {10.1088/0266-5611/19/6/057},
       URL = {https://doi.org/10.1088/0266-5611/19/6/057},
}


@article {minimalsurface,
    AUTHOR = {Nurminen, Janne},
     TITLE = {An inverse problem for the minimal surface equation},
   JOURNAL = {Nonlinear Anal.},
    VOLUME = {227},
      YEAR = {2023},
     PAGES = {Paper No. 113163, 19},
      ISSN = {0362-546X},
       DOI = {10.1016/j.na.2022.113163},
       URL = {https://doi.org/10.1016/j.na.2022.113163},
}


@article {quasilinear2,
    AUTHOR = {C\^{a}rstea, C\u{a}t\u{a}lin I. and Feizmohammadi, Ali and Kian, Yavar and
              Krupchyk, Katya and Uhlmann, Gunther},
     TITLE = {The {C}alder\'{o}n inverse problem for isotropic quasilinear
              conductivities},
   JOURNAL = {Adv. Math.},
    VOLUME = {391},
      YEAR = {2021},
     PAGES = {Paper No. 107956, 31},
      ISSN = {0001-8708},
       DOI = {10.1016/j.aim.2021.107956},
       URL = {https://doi.org/10.1016/j.aim.2021.107956},
}


@article {nonlinearmaxwell,
    AUTHOR = {Assylbekov, Yernat M. and Zhou, Ting},
     TITLE = {Inverse problems for nonlinear {M}axwell's equations with
              second harmonic generation},
   JOURNAL = {J. Differential Equations},
    VOLUME = {296},
      YEAR = {2021},
     PAGES = {148--169},
      ISSN = {0022-0396},
       DOI = {10.1016/j.jde.2021.06.002},
       URL = {https://doi.org/10.1016/j.jde.2021.06.002},
}
		


@article {quasilinear,
    AUTHOR = {C\^{a}rstea, C\u{a}t\u{a}lin I. and Feizmohammadi, Ali},
     TITLE = {An inverse boundary value problem for certain anisotropic
              quasilinear elliptic equations},
   JOURNAL = {J. Differential Equations},
    VOLUME = {284},
      YEAR = {2021},
     PAGES = {318--349},
      ISSN = {0022-0396},
       DOI = {10.1016/j.jde.2021.02.044},
       URL = {https://doi.org/10.1016/j.jde.2021.02.044},
}

@article {Iterative,
    AUTHOR = {Gutman, Semion and Klibanov, Michael},
     TITLE = {Iterative method for multi-dimensional inverse scattering
              problems at fixed frequencies},
   JOURNAL = {Inverse Problems},
    VOLUME = {10},
      YEAR = {1994},
    NUMBER = {3},
     PAGES = {573--599},
      ISSN = {0266-5611},
       URL = {http://stacks.iop.org/0266-5611/10/573},
}


@article {Hohage,
    AUTHOR = {Hohage, Thorsten},
     TITLE = {On the numerical solution of a three-dimensional inverse
              medium scattering problem},
   JOURNAL = {Inverse Problems},
    VOLUME = {17},
      YEAR = {2001},
    NUMBER = {6},
     PAGES = {1743--1763},
      ISSN = {0266-5611},
       DOI = {10.1088/0266-5611/17/6/314},
       URL = {https://doi.org/10.1088/0266-5611/17/6/314},
}
		



@book {Factorization,
    AUTHOR = {Kirsch, Andreas and Grinberg, Natalia},
     TITLE = {The factorization method for inverse problems},
    SERIES = {Oxford Lecture Series in Mathematics and its Applications},
    VOLUME = {36},
 PUBLISHER = {Oxford University Press, Oxford},
      YEAR = {2008},
     PAGES = {xiv+201},
      ISBN = {978-0-19-921353-5},
}
		


@article {Rondi,
    AUTHOR = {Di Cristo, Michele and Rondi, Luca},
     TITLE = {Examples of exponential instability for inverse inclusion and
              scattering problems},
   JOURNAL = {Inverse Problems},
  FJOURNAL = {Inverse Problems. An International Journal on the Theory and
              Practice of Inverse Problems, Inverse Methods and Computerized
              Inversion of Data},
    VOLUME = {19},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {685--701},
      ISSN = {0266-5611},
       DOI = {10.1088/0266-5611/19/3/313},
       URL = {https://doi.org/10.1088/0266-5611/19/3/313},
}

@book {Eskin,
    AUTHOR = {Eskin, Gregory},
     TITLE = {Lectures on linear partial differential equations},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {123},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2011},
     PAGES = {xviii+410},
      ISBN = {978-0-8218-5284-2},
       DOI = {10.1090/gsm/123},
       URL = {https://doi.org/10.1090/gsm/123},
}


@book {CKv4,
    AUTHOR = {Colton, David and Kress, Rainer},
     TITLE = {Inverse acoustic and electromagnetic scattering theory},
    SERIES = {Applied Mathematical Sciences},
    VOLUME = {93},
      NOTE = {Fourth edition of [ MR1183732]},
 PUBLISHER = {Springer, Cham},
      YEAR = {2019},
      ISBN = {978-3-030-30350-1; 978-3-030-30351-8},
       DOI = {10.1007/978-3-030-30351-8},
       URL = {https://doi.org/10.1007/978-3-030-30351-8},
}


@article {Hormander_rellich,
    AUTHOR = {H\"{o}rmander, Lars},
     TITLE = {Lower bounds at infinity for solutions of differential
              equations with constant coefficients},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {16},
      YEAR = {1973},
     PAGES = {103--116},
       DOI = {10.1007/BF02761975},
       URL = {https://doi.org/10.1007/BF02761975},
}


@article {Novikov,
    AUTHOR = {Novikov, R. G.},
     TITLE = {A multidimensional inverse spectral problem for the equation
              {$-\Delta\psi +(v(x)-Eu(x))\psi=0$}},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u{\i} Analiz i ego
              Prilozheniya},
    VOLUME = {22},
      YEAR = {1988},
    NUMBER = {4},
     PAGES = {11--22, 96},
      ISSN = {0374-1990},
       DOI = {10.1007/BF01077418},
       URL = {https://doi.org/10.1007/BF01077418},
}




@article {Nachman,
    AUTHOR = {Nachman, Adrian I.},
     TITLE = {Reconstructions from boundary measurements},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {128},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {531--576},
      ISSN = {0003-486X},
       DOI = {10.2307/1971435},
       URL = {https://doi.org/10.2307/1971435},
}


@misc{ST22,
  doi = {10.48550/ARXIV.2202.05290},
  url = {https://arxiv.org/abs/2202.05290},
  author = {Salo, Mikko and Tzou, Leo},
  title = {Inverse problems for semilinear elliptic PDE with measurements at a single point},
  publisher = {arXiv},
  year = {2022},
}

@incollection {KS14,
    AUTHOR = {Kenig, Carlos and Salo, Mikko},
     TITLE = {Recent progress in the {C}alder\'{o}n problem with partial data},
 BOOKTITLE = {Inverse problems and applications},
    SERIES = {Contemp. Math.},
    VOLUME = {615},
     PAGES = {193--222},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2014},
       DOI = {10.1090/conm/615/12245},
       URL = {https://doi.org/10.1090/conm/615/12245},
}



@article {IUY10,
    AUTHOR = {Imanuvilov, Oleg Yu. and Uhlmann, Gunther and Yamamoto,
              Masahiro},
     TITLE = {The {C}alder\'{o}n problem with partial data in two dimensions},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {23},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {655--691},
      ISSN = {0894-0347},
   MRCLASS = {35R30 (35J10 35Q60)},
  MRNUMBER = {2629983},
MRREVIEWER = {Patricia Gaitan},
       DOI = {10.1090/S0894-0347-10-00656-9},
       URL = {https://doi.org/10.1090/S0894-0347-10-00656-9},
}



@article {AMRE17,
    AUTHOR = {Alessandrini, Giovanni and de Hoop, Maarten V. and Gaburro,
              Romina and Sincich, Eva},
     TITLE = {Lipschitz stability for the electrostatic inverse boundary
              value problem with piecewise linear conductivities},
   JOURNAL = {J. Math. Pures Appl. (9)},
  FJOURNAL = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es. Neuvi\`eme S\'{e}rie},
    VOLUME = {107},
      YEAR = {2017},
    NUMBER = {5},
     PAGES = {638--664},
      ISSN = {0021-7824},
       DOI = {10.1016/j.matpur.2016.10.001},
       URL = {https://doi.org/10.1016/j.matpur.2016.10.001},
}


@article {BMQ13,
    AUTHOR = {Beretta, Elena and de Hoop, Maarten V. and Qiu, Lingyun},
     TITLE = {Lipschitz stability of an inverse boundary value problem for a
              {S}chr\"{o}dinger-type equation},
   JOURNAL = {SIAM J. Math. Anal.},
  FJOURNAL = {SIAM Journal on Mathematical Analysis},
    VOLUME = {45},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {679--699},
      ISSN = {0036-1410},
       DOI = {10.1137/120869201},
       URL = {https://doi.org/10.1137/120869201},
}


@article {AV05,
    AUTHOR = {Alessandrini, Giovanni and Vessella, Sergio},
     TITLE = {Lipschitz stability for the inverse conductivity problem},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {35},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {207--241},
      ISSN = {0196-8858},
       DOI = {10.1016/j.aam.2004.12.002},
       URL = {https://doi.org/10.1016/j.aam.2004.12.002},
}





@article {KU19,
    AUTHOR = {Krupchyk, Katya and Uhlmann, Gunther},
     TITLE = {Stability estimates for partial data inverse problems for
              {S}chr\"{o}dinger operators in the high frequency limit},
   JOURNAL = {J. Math. Pures Appl. (9)},
  FJOURNAL = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es. Neuvi\`eme S\'{e}rie},
    VOLUME = {126},
      YEAR = {2019},
     PAGES = {273--291},
      ISSN = {0021-7824},
       DOI = {10.1016/j.matpur.2019.02.017},
       URL = {https://doi.org/10.1016/j.matpur.2019.02.017},
}



@article {AU04,
    AUTHOR = {Ammari, Habib and Uhlmann, Gunther},
     TITLE = {Reconstruction of the potential from partial {C}auchy data for
              the {S}chr\"{o}dinger equation},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {53},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {169--183},
      ISSN = {0022-2518},
       DOI = {10.1512/iumj.2004.53.2299},
       URL = {https://doi.org/10.1512/iumj.2004.53.2299},
}


@article {KV2,
    AUTHOR = {Kohn, Robert and Vogelius, Michael},
     TITLE = {Determining conductivity by boundary measurements},
   JOURNAL = {Comm. Pure Appl. Math.},
  FJOURNAL = {Communications on Pure and Applied Mathematics},
    VOLUME = {37},
      YEAR = {1984},
    NUMBER = {3},
     PAGES = {289--298},
      ISSN = {0010-3640},
       DOI = {10.1002/cpa.3160370302},
       URL = {https://doi.org/10.1002/cpa.3160370302},
}

@article{Cheng2019,
  title={偏微分方程反问题: 模型, 算法和应用},
  author={程晋 and 刘继军 and 张波},
  journal={中国科学: 数学},
  VOLUME = {49},
  number={4},
  pages={643--666},
  year={2019}
}


@incollection {KV1,
    AUTHOR = {Kohn, Robert V. and Vogelius, Michael},
     TITLE = {Identification of an unknown conductivity by means of
              measurements at the boundary},
 BOOKTITLE = {Inverse problems ({N}ew {Y}ork, 1983)},
    SERIES = {SIAM-AMS Proc.},
    VOLUME = {14},
     PAGES = {113--123},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1984},
       DOI = {10.1002/cpa.3160370302},
       URL = {https://doi.org/10.1002/cpa.3160370302},
}
		



@incollection {CalderonEIT,
    AUTHOR = {Calder\'{o}n, Alberto-P.},
     TITLE = {On an inverse boundary value problem},
 BOOKTITLE = {Seminar on {N}umerical {A}nalysis and its {A}pplications to
              {C}ontinuum {P}hysics ({R}io de {J}aneiro, 1980)},
     PAGES = {65--73},
 PUBLISHER = {Soc. Brasil. Mat., Rio de Janeiro},
      YEAR = {1980},
}




@book{Math2019,
    AUTHOR = {Bourl\`es, Henri},
     TITLE = {Fundamentals of advanced mathematics 3. {D}ifferential
              calculus, tensor calculus, differential geometry, global
              analysis},
      NOTE = {New mathematical methods, systems and applications set},
 PUBLISHER = {ISTE Press, London; Elsevier Ltd, Oxford},
      YEAR = {2019},
      ISBN = {978-1-78548-250-2},
}



@book{SobolevEuiv,
    AUTHOR = {Haroske, Dorothee D. and Triebel, Hans},
     TITLE = {Distributions, {S}obolev spaces, elliptic equations},
    SERIES = {EMS Textbooks in Mathematics},
 PUBLISHER = {European Mathematical Society (EMS), Z\"{u}rich},
      YEAR = {2008},
      ISBN = {978-3-03719-042-5},
   MRCLASS = {46-02 (35B45 35J25 46E35 46F05)},
  MRNUMBER = {2375667},
}




@book{StrongElliptic,
    AUTHOR = {McLean, W},
     TITLE = {Strongly elliptic systems and boundary integral equations},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2000},
      ISBN = {0-521-66332-6; 0-521-66375-X},
   MRCLASS = {35J45 (47F05 47G10 47N20 65N38)},
  MRNUMBER = {1742312},
}




@book {FollandFourier,
    AUTHOR = {Folland, G B},
     TITLE = {Fourier analysis and its applications},
    SERIES = {The Wadsworth \& Brooks/Cole Mathematics Series},
 PUBLISHER = {Wadsworth \& Brooks/Cole Advanced Books \& Software, Pacific
              Grove, CA},
      YEAR = {1992},
      ISBN = {0-534-17094-3},
   MRCLASS = {42-01 (00A05 33-01 34B05 34L10 44A10 46-01)},
  MRNUMBER = {1145236}
}




@book{EllipticParabolic,
    AUTHOR = {Wu, Z and Yin, J and Wang, C},
     TITLE = {Elliptic \& parabolic equations},
 PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ},
      YEAR = {2006},
      ISBN = {981-270-026-9},
       DOI = {10.1142/6238},
       URL = {https://doi.org/10.1142/6238}
}

@book{DirectElliptic,
    AUTHOR = {Ne\v{c}as, J},
     TITLE = {Direct methods in the theory of elliptic equations},
    SERIES = {Springer Monographs in Mathematics},
 PUBLISHER = {Springer, Heidelberg},
      YEAR = {2012},
      ISBN = {978-3-642-10454-1; 978-3-642-10455-8},
   MRCLASS = {35-02 (35J08 35J20 35J25 35J50 35J57)},
  MRNUMBER = {3014461},
MRREVIEWER = {Norbert Ortner},
       DOI = {10.1007/978-3-642-10455-8},
       URL = {https://doi.org/10.1007/978-3-642-10455-8}
}
	
@book{RR2004,
    AUTHOR = {Renardy, M and Rogers, R C},
     TITLE = {An introduction to partial differential equations},
    SERIES = {Texts in Applied Mathematics},
    VOLUME = {13},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2004},
      ISBN = {0-387-00444-0},
   MRCLASS = {35-01 (46N20 47F05 47N20)},
  MRNUMBER = {2028503}
}

@book{GuoFunctional,
	AUTHOR =  {郭坤宇},
	TITLE  = {算子理论基础},
	EDITION =  {第二版},
	PUBLISHER = {上海：复旦大学出版社},
	YEAR = {2022}
}


@book{ChenPDE,
    AUTHOR = {陈恕行},
     TITLE = {现代偏微分方程导论},
     EDITION = {第二版},
 PUBLISHER = {北京：科学出版社},
      YEAR = {2018}
}


@book{Chen2elliptic,
    AUTHOR = {陈亚浙，吴兰成 },
     TITLE = {二阶椭圆型方程与椭圆型方程组},
 PUBLISHER = {北京：科学出版社},
      YEAR = {1997}
}


@book{Chern,
    AUTHOR = {陈省身，陈维桓 },
     TITLE = {微分几何讲义},
 PUBLISHER = {北京：北京大学出版社},
      YEAR = {1999}
}



@book{FractionalSobolev,
    AUTHOR = {Edmunds, D E and Evans, W D},
     TITLE = {Fractional {S}obolev spaces and inequalities},
    SERIES = {Cambridge Tracts in Mathematics},
    VOLUME = {230},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2023},
      ISBN = {978-1-009-25463-2},
   MRCLASS = {46-02 (26A33 35-02 46E35)},
  MRNUMBER = {4480576}
}

@book{LeoniSobolev,
    AUTHOR = {Leoni, G},
     TITLE = {A first course in {S}obolev spaces},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {105},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2009},
      ISBN = {978-0-8218-4768-8},
  MRNUMBER = {2527916},
MRREVIEWER = {Dorothee D. Haroske},
       DOI = {10.1090/gsm/105},
       URL = {https://doi.org/10.1090/gsm/105}
}


@book{boyd2020nonlinear,
  title={Nonlinear optics},
  author={Boyd, Robert W},
  year={2020},
  edition = {Fourth},
  publisher={Academic press}
}


@book {Yaf10ScatteringAnalyticTheory,
    AUTHOR = {Yafaev, D. R.},
     TITLE = {Mathematical scattering theory},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {158},
      NOTE = {Analytic theory},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2010},
       DOI = {10.1090/surv/158},
       URL = {https://doi.org/10.1090/surv/158},
}


@article {GMMR12InverseScattering,
    AUTHOR = {Grisel, Y. and Mouysset, V. and Mazet, P.-A. and Raymond,
              J.-P.},
     TITLE = {Determining the shape of defects in non-absorbing
              inhomogeneous media from far-field measurements},
   JOURNAL = {Inverse Problems},
  FJOURNAL = {Inverse Problems. An International Journal on the Theory and
              Practice of Inverse Problems, Inverse Methods and Computerized
              Inversion of Data},
    VOLUME = {28},
      YEAR = {2012},
    NUMBER = {5},
     PAGES = {055003, 19},
       DOI = {10.1088/0266-5611/28/5/055003},
       URL = {https://doi.org/10.1088/0266-5611/28/5/055003},
}






@book{Lee13SmoothManifold,
    author = {Lee, J M},
     title = {Introduction to smooth manifolds},
   edition = {Second},
 publisher = {Springer, New York},
      year = {2013},
      note = {\href{https://mathscinet.ams.org/mathscinet-getitem?mr=2954043}{MR2954043}, \href{https://doi.org/10.1007/978-1-4419-9982-5}{doi:10.1007/978-1-4419-9982-5}}
}

@book {Chavel06RiemannianGeometry,
    AUTHOR = {Chavel, Isaac},
     TITLE = {Riemannian geometry},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {98},
   EDITION = {Second},
      NOTE = {A modern introduction},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2006},
       DOI = {10.1017/CBO9780511616822},
       URL = {https://doi.org/10.1017/CBO9780511616822},
}
		

@article {KRS,
    AUTHOR = {Koch, Herbert and R\"{u}land, Angkana and Salo, Mikko},
     TITLE = {On instability mechanisms for inverse problems},
   JOURNAL = {Ars Inven. Anal.},
  FJOURNAL = {Ars Inveniendi Analytica},
      YEAR = {2021},
     PAGES = {Paper No. 7, 93},
}

@book {RiemannOpt,
    AUTHOR = {Sato, Hiroyuki},
     TITLE = {Riemannian optimization and its applications},
    SERIES = {SpringerBriefs in Electrical and Computer Engineering},
      NOTE = {SpringerBriefs in Control, Automation and Robotics},
 PUBLISHER = {Springer, Cham},
      YEAR = {2021},
       DOI = {10.1007/978-3-030-62391-3},
       URL = {https://doi.org/10.1007/978-3-030-62391-3},
}
		

@book{EG92MeasureTheory,
    author = {Evans, L C and Gariepy, R F},
    title = {Measure theory and fine properties of functions},
    edition = {first},
    series = {Studies in Advanced Mathematics},
    publisher = {CRC Press},
    address = {Boca Raton, FL},
    year = {1992},
    note = {\href{https://mathscinet.ams.org/mathscinet-getitem?mr=1158660}{MR1158660}}
}


@article{Ale88,
author = {Alessandrini, G},
title = {Stable determination of conductivity by boundary measurements},
journal = {Applicable Analysis},
volume = {27},
number = {1-3},
pages = {153-172},
year  = {1988},
publisher = {Taylor \& Francis},
doi = {10.1080/00036818808839730},
URL = {https://doi.org/10.1080/00036818808839730}
}


@book{AF2003,
    AUTHOR = {Adams, R A and Fournier, J J F},
     TITLE = {Sobolev spaces},
    SERIES = {Pure and Applied Mathematics (Amsterdam)},
    VOLUME = {140},
   EDITION = {Second},
 PUBLISHER = {Elsevier/Academic Press, Amsterdam},
      YEAR = {2003},
      ISBN = {0-12-044143-8},
   MRCLASS = {46E35 (46-01 46-02 46B70 46Exx)},
  MRNUMBER = {2424078},
}



@article{CFKKU,
title = {The Calder\'on inverse problem for isotropic quasilinear conductivities},
journal = {Advances in Mathematics},
volume = {391},
pages = {107956},
year = {2021},
issn = {0001-8708},
doi = {10.1016/j.aim.2021.107956},
url = {https://www.sciencedirect.com/science/article/pii/S0001870821003959},
author = {C\^{a}rstea, C I and Feizmohammadi, A and Kian, Y and Krupchyk, K and Uhlmann, G}
}


@misc{CFO2022remark,
  doi = {10.48550/ARXIV.2204.02442},  
  url = {https://arxiv.org/abs/2204.02442}, 
  author = {C\^arstea, C I and Feizmohammadi, A and Oksanen, L}, 
  title = {Remarks on the anisotropic Calder\'on problem},
  publisher = {arXiv},
  year = {2022}
}


@article{CIL2016jde,
title = {Increasing stability in the inverse source problem with many frequencies},
journal = {Journal of Differential Equations},
volume = {260},
number = {5},
pages = {4786-4804},
year = {2016},
issn = {0022-0396},
doi = {10.1016/j.jde.2015.11.030},
url = {https://www.sciencedirect.com/science/article/pii/S0022039615006476},
author = {Cheng, J and Isakov, V and Lu, S}
}

@misc{FLL21,
  doi = {10.48550/ARXIV.2112.08305},
  url = {https://arxiv.org/abs/2112.08305},
  author = {Feizmohammadi, A and Liimatainen, T and Lin, Y-H},
  title = {An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds},
  publisher = {arXiv},
  year = {2021}
}

@article{FO20jde,
title = {An inverse problem for a semi-linear elliptic equation in Riemannian geometries},
journal = {Journal of Differential Equations},
volume = {269},
number = {6},
pages = {4683-4719},
year = {2020},
issn = {0022-0396},
doi = {10.1016/j.jde.2020.03.037},
url = {https://www.sciencedirect.com/science/article/pii/S0022039620301510},
author = {Feizmohammadi, A and Oksanen, L}
}


@article{FT05numerical,
title = {Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions},
journal = {Journal of Computational Physics},
volume = {210},
number = {1},
pages = {183-224},
year = {2005},
issn = {0021-9991},
doi = {10.1016/j.jcp.2005.04.015},
url = {https://www.sciencedirect.com/science/article/pii/S0021999105002068},
author = {Fibich, G and Tsynkov, S}
}


@book {GT2001,
    AUTHOR = {Gilbarg, D and Trudinger, N S},
     TITLE = {Elliptic partial differential equations of second order},
    SERIES = {Classics in Mathematics},
      NOTE = {Reprint of the 1998 edition},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2001},
      ISBN = {3-540-41160-7},
   MRCLASS = {35-02 (35Jxx)},
  MRNUMBER = {1814364},
}


@book {Combinatorics96,
     TITLE = {Handbook of combinatorics. {V}ol. 2},
    EDITOR = {Graham, R L and Gr\"{o}tschel, M and Lov\'{a}sz, L},
 PUBLISHER = {Elsevier Science B.V., Amsterdam; MIT Press, Cambridge, MA},
      YEAR = {1995},
      ISBN = {0-444-88002-X},
   MRCLASS = {05-06 (00A20 05-00)},
  MRNUMBER = {1373655},
}



@article {Isakov93nonlinear,
    AUTHOR = {Isakov, V},
     TITLE = {On uniqueness in inverse problems for semilinear parabolic
              equations},
   JOURNAL = {Arch. Rational Mech. Anal.},
  FJOURNAL = {Archive for Rational Mechanics and Analysis},
    VOLUME = {124},
      YEAR = {1993},
    NUMBER = {1},
     PAGES = {1--12},
      ISSN = {0003-9527},
       DOI = {10.1007/BF00392201},
       URL = {https://doi.org/10.1007/BF00392201},
}

@article{Isakov11increasing,
title = {Increasing stability for the Schr\"odinger potential from the Dirichlet-to Neumann map},
journal = {Discrete and Continuous Dynamical Systems - S},
volume = {4},number = {3},pages = {631-640},
year = {2011},
issn = {1937-1632},
doi = {10.3934/dcdss.2011.4.631},
url = {https://www.aimsciences.org/article/doi/10.3934/dcdss.2011.4.631},
author = {Isakov, V}
}



@incollection {Isakov2015scattering,
    AUTHOR = {Isakov, V},
     TITLE = {Increasing stability for near field from the scattering
              amplitude},
 BOOKTITLE = {Spectral theory and partial differential equations},
    SERIES = {Contemp. Math.},
    VOLUME = {640},
     PAGES = {59--70},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2015},
       DOI = {10.1090/conm/640/12839},
       URL = {https://doi.org/10.1090/conm/640/12839},
}

@article{ILX2020linearized,
author = {Isakov, V and Lu, S and Xu, B},
title = {Linearized Inverse Schr\"odinger Potential Problem at a Large Wavenumber},
journal = {SIAM Journal on Applied Mathematics},
volume = {80},
number = {1},
pages = {338-358},
year = {2020},
doi = {10.1137/18M1226932},
URL = {https://doi.org/10.1137/18M1226932}
}



@article{ILX2022Maxwell,
title = {A linearised inverse conductivity problem for the Maxwell system at a high frequency},
journal = {Journal of Computational Physics},
volume = {455},
pages = {111003},
year = {2022},
issn = {0021-9991},
doi = {10.1016/j.jcp.2022.111003},
url = {https://www.sciencedirect.com/science/article/pii/S0021999122000651},
author = {Isakov, V and Lu, S and Xu, B}
}

@article{IS1994nonlinear,
author = {Isakov, V and Sylvester, J},
title = {Global uniqueness for a semilinear elliptic inverse problem},
journal = {Communications on Pure and Applied Mathematics},
volume = {47},
number = {10},
pages = {1403-1410},
doi = {10.1002/cpa.3160471005},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160471005},
year = {1994}
}


@article{KUW2021instability,
author = {Kow, P-Z and Uhlmann, G and Wang, J-N},
title = {Optimality of Increasing Stability for an Inverse Boundary Value Problem},
journal = {SIAM Journal on Mathematical Analysis},
volume = {53},
number = {6},
pages = {7062-7080},
year = {2021},
doi = {10.1137/21M1402169},
URL = {https://doi.org/10.1137/21M1402169}
}

@article{KLU2018nonlinear,
author={Kurylev, Y
and Lassas, M
and Uhlmann, G},
title={Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations},
journal={Inventiones mathematicae},
year={2018},
volume={212},
number={3},
pages={781-857},
issn={1432-1297},
doi={10.1007/s00222-017-0780-y},
url={https://doi.org/10.1007/s00222-017-0780-y}
}

@article{LL2019fractional-semilinear,
author={Lai,R-y and Lin, Y-H},
title={Global uniqueness for the fractional semilinear Schr\"odinger equation},
journal={Proceedings of the American Mathematical Society},
year={2019},
volumn={147},
pages={1189-1199},
doi={10.1090/proc/14319},
url={https://www.ams.org/journals/proc/2019-147-03/S0002-9939-2018-14319-1}
}

@article {Vessella99continuation,
    AUTHOR = {Vessella, Sergio},
     TITLE = {A continuous dependence result in the analytic continuation
              problem},
   JOURNAL = {Forum Math.},
  FJOURNAL = {Forum Mathematicum},
    VOLUME = {11},
      YEAR = {1999},
    NUMBER = {6},
     PAGES = {695--703},
      ISSN = {0933-7741},
       DOI = {10.1515/form.1999.020},
       URL = {https://doi.org/10.1515/form.1999.020},
}


@article{LLLS2021power,
title = {Inverse problems for elliptic equations with power type nonlinearities},
journal = {Journal de Mathématiques Pures et Appliquées},
volume = {145},
pages = {44-82},
year = {2021},
issn = {0021-7824},
doi = {10.1016/j.matpur.2020.11.006},
url = {https://www.sciencedirect.com/science/article/pii/S0021782420301902},
author = {Lassas, M and Liimatainen, T and Lin, Y-H and Salo, M}
}

@article{LLLS2021semilinear-partial-data,
title = {Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations},
volume = {37},
pages = {1553-1580},
year = {2021},
number = {4},
doi = {10.4171/RMI/1242},
url = {https://ems.press/journals/rmi/articles/17335},
author = {Lassas, M and Liimatainen, T and Lin, Y-H and Salo, M},
journal = {Revista Matem\'atica Iberoamericana}
}


@article{LLPT2022same,
title = {Uniqueness, reconstruction and stability for an inverse problem of a semi-linear wave equation},
journal = {Journal of Differential Equations},
volume = {337},
pages = {395-435},
year = {2022},
issn = {0022-0396},
doi = {10.1016/j.jde.2022.08.010},
url = {https://www.sciencedirect.com/science/article/pii/S002203962200482X},
author = {Lassas, M and Liimatainen, T and Potenciano-Machado, L and Tyni, T},
}


@article {GuntherNonlinear,
    AUTHOR = {Kurylev, Yaroslav and Lassas, Matti and Uhlmann, Gunther},
     TITLE = {Inverse problems for {L}orentzian manifolds and non-linear
              hyperbolic equations},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {212},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {781--857},
      ISSN = {0020-9910},
       DOI = {10.1007/s00222-017-0780-y},
       URL = {https://doi.org/10.1007/s00222-017-0780-y},
}


@article {ZZ17,
    AUTHOR = {Zhang, Bo and Zhang, Haiwen},
     TITLE = {Recovering scattering obstacles by multi-frequency phaseless
              far-field data},
   JOURNAL = {J. Comput. Phys.},
  FJOURNAL = {Journal of Computational Physics},
    VOLUME = {345},
      YEAR = {2017},
     PAGES = {58--73},
      ISSN = {0021-9991},
       DOI = {10.1016/j.jcp.2017.05.022},
       URL = {https://doi.org/10.1016/j.jcp.2017.05.022},
}

@article {WGZL17,
    AUTHOR = {Wang, Xianchao and Guo, Yukun and Zhang, Deyue and Liu,
              Hongyu},
     TITLE = {Fourier method for recovering acoustic sources from
              multi-frequency far-field data},
   JOURNAL = {Inverse Problems},
    VOLUME = {33},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {035001, 18},
      ISSN = {0266-5611},
       DOI = {10.1088/1361-6420/aa573c},
       URL = {https://doi.org/10.1088/1361-6420/aa573c},
}

@article {IL18,
    AUTHOR = {Isakov, Victor and Lu, Shuai},
     TITLE = {Increasing stability in the inverse source problem with
              attenuation and many frequencies},
   JOURNAL = {SIAM J. Appl. Math.},
  FJOURNAL = {SIAM Journal on Applied Mathematics},
    VOLUME = {78},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {1--18},
      ISSN = {0036-1399},
       DOI = {10.1137/17M1112704},
       URL = {https://doi.org/10.1137/17M1112704},
}

@article {ZL19,
    AUTHOR = {Zhao, Yue and Li, Peijun},
     TITLE = {Stability on the one-dimensional inverse source scattering
              problem in a two-layered medium},
   JOURNAL = {Appl. Anal.},
  FJOURNAL = {Applicable Analysis. An International Journal},
    VOLUME = {98},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {682--692},
      ISSN = {0003-6811},
       DOI = {10.1080/00036811.2017.1399365},
       URL = {https://doi.org/10.1080/00036811.2017.1399365},
}

@article {BL05,
    AUTHOR = {Bao, Gang and Li, Peijun},
     TITLE = {Inverse medium scattering for the {H}elmholtz equation at
              fixed frequency},
   JOURNAL = {Inverse Problems},
    VOLUME = {21},
      YEAR = {2005},
    NUMBER = {5},
     PAGES = {1621--1641},
      ISSN = {0266-5611},
       DOI = {10.1088/0266-5611/21/5/007},
       URL = {https://doi.org/10.1088/0266-5611/21/5/007},
}


@article {FT2005,
    AUTHOR = {Fibich, G. and Tsynkov, S.},
     TITLE = {Numerical solution of the nonlinear {H}elmholtz equation using
              nonorthogonal expansions},
   JOURNAL = {J. Comput. Phys.},
  FJOURNAL = {Journal of Computational Physics},
    VOLUME = {210},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {183--224},
      ISSN = {0021-9991},
       DOI = {10.1016/j.jcp.2005.04.015},
       URL = {https://doi.org/10.1016/j.jcp.2005.04.015},
}

@article {YL2017,
    AUTHOR = {Yuan, Lijun and Lu, Ya Yan},
     TITLE = {Robust iterative method for nonlinear {H}elmholtz equation},
   JOURNAL = {J. Comput. Phys.},
  FJOURNAL = {Journal of Computational Physics},
    VOLUME = {343},
      YEAR = {2017},
     PAGES = {1--9},
      ISSN = {0021-9991},
       DOI = {10.1016/j.jcp.2017.04.046},
       URL = {https://doi.org/10.1016/j.jcp.2017.04.046},
}

@article{F1966,
AUTHOR = {L D Faddeev},
TITLE = {Increasing solutions of the Schr\"{o}dinger equation},
JOURNAL = {Dokl. Akad. Nauk SSSR},
YEAR = {1965},
VOLUME = {165},
issue ={3},
pages = {514--517}
}


%-------------------------------------------------------------------------

@article{LSX2022power,
doi = {10.1088/1361-6420/ac637a},
url = {https://dx.doi.org/10.1088/1361-6420/ac637a},
year = {2022},
publisher = {IOP Publishing},
volume = {38},
number = {6},
pages = {065009},
author = {Lu, S and Salo, M and Xu, B},
title = {Increasing stability in the linearized inverse Schr\"odinger potential problem with power type nonlinearities},
journal = {Inverse Problems}
}

@article{Mandache2001,
doi = {10.1088/0266-5611/17/5/313},
url = {https://dx.doi.org/10.1088/0266-5611/17/5/313},
year = {2001},
volume = {17},
number = {5},
pages = {1435},
author = {Mandache, N},
title = {Exponential instability in an inverse
problem for the Schr\"odinger equation},
journal = {Inverse Problems},
}



@article{NUW2013acoustic,
doi = {10.1088/0266-5611/29/2/025012},
url = {https://dx.doi.org/10.1088/0266-5611/29/2/025012},
year = {2013},
publisher = {IOP Publishing},
volume = {29},
number = {2},
pages = {025012},
author = {Nagayasu, S and Uhlmann, G and Wang, J-N},
title = {Increasing stability in an inverse problem for the acoustic equation},
journal = {Inverse Problems}
}




@article{Nur2022,
title = {Determining an unbounded potential for an elliptic equation with a power type nonlinearity},
journal = {Journal of Mathematical Analysis and Applications},
pages = {126962},
year = {2023},
issn = {0022-247X},
doi = {https://doi.org/10.1016/j.jmaa.2022.126962},
url = {https://www.sciencedirect.com/science/article/pii/S0022247X22009763},
author = {Nurminen, J}
}


@article{SZ2012plaplacian,
author = {Salo, M and Zhong, X},
title = {An Inverse Problem for the $p$-Laplacian: Boundary Determination},
journal = {SIAM Journal on Mathematical Analysis},
volume = {44},
number = {4},
pages = {2474-2495},
year = {2012},
doi = {10.1137/110838224},
URL = {https://doi.org/10.1137/110838224}
}

@article{SI2007,
doi = {10.1088/0266-5611/23/4/019},
url = {https://dx.doi.org/10.1088/0266-5611/23/4/019},
year = {2007},
volume = {23},
number = {4},
pages = {1689},
author = {Subbarayappa, D A and Isakov, V},
title = {On increased stability in the continuation of the Helmholtz equation},
journal = {Inverse Problems}
}

@article{SU1997nonlinear,
title = {Inverse problems in quasilinear anisotropic media},
author = {Sun, Z and Uhlmann, G},
volume = {119},
number = {4},
year = {1997},
pages = {771-797},
journal = {American Journal of Mathematics},
doi = {10.1353/ajm.1997.0027},
url = {https://muse.jhu.edu/article/758/pdf}
}


@article {Sun10,
    AUTHOR = {Sun, Ziqi},
     TITLE = {An inverse boundary-value problem for semilinear elliptic
              equations},
   JOURNAL = {Electron. J. Differential Equations},
  FJOURNAL = {Electronic Journal of Differential Equations},
      YEAR = {2010},
     PAGES = {No. 37, 5},
}

@article {IN95,
    AUTHOR = {Isakov, Victor and Nachman, Adrian I.},
     TITLE = {Global uniqueness for a two-dimensional semilinear elliptic
              inverse problem},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {347},
      YEAR = {1995},
    NUMBER = {9},
     PAGES = {3375--3390},
      ISSN = {0002-9947},
       DOI = {10.2307/2155015},
       URL = {https://doi.org/10.2307/2155015},
}


@article {IY13,
    AUTHOR = {Imanuvilov, Oleg and Yamamoto, Masahiro},
     TITLE = {Unique determination of potentials and semilinear terms of
              semilinear elliptic equations from partial {C}auchy data},
   JOURNAL = {J. Inverse Ill-Posed Probl.},
  FJOURNAL = {Journal of Inverse and Ill-Posed Problems},
    VOLUME = {21},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {85--108},
      ISSN = {0928-0219},
       DOI = {10.1515/jip-2012-0033},
       URL = {https://doi.org/10.1515/jip-2012-0033},
}
		


@article{WZ2018numerical,
author = {Wu, H and Zou, J},
title = {Finite Element Method and its Analysis for a Nonlinear Helmholtz Equation with High Wave Numbers},
journal = {SIAM Journal on Numerical Analysis},
volume = {56},
number = {3},
pages = {1338-1359},
year = {2018},
doi = {10.1137/17M111314X},
URL = {https://doi.org/10.1137/17M111314X}
}

@article{XB2010,
author = {Xu, Z and Bao, G},
journal = {Journal of the Optical Society of America A},
number = {11},
pages = {2347--2353},
publisher = {Optica Publishing Group},
title = {A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects},
volume = {27},
year = {2010},
url = {https://opg.optica.org/josaa/abstract.cfm?URI=josaa-27-11-2347},
doi = {10.1364/JOSAA.27.002347}
}

@article{Y20171,
title = {Robust iterative method for nonlinear Helmholtz equation},
journal = {Journal of Computational Physics},
volume = {343},
pages = {1-9},
year = {2017},
issn = {0021-9991},
doi = {10.1016/j.jcp.2017.04.046},
url = {https://www.sciencedirect.com/science/article/pii/S002199911730325X},
author = {Yuan, L and Lu, Y Y}
}

@article{ZLX2022IPI,
title = {Linearized inverse Schr\"odinger potential problem with partial data and its deep neural network inversion},
journal = {Inverse Problems and Imaging},
volume = {16},number = {6},pages = {1669-1690},
year = {2022},
issn = {1930-8337},
doi = {10.3934/ipi.2022045},
url = {https://www.aimsciences.org//article/doi/10.3934/ipi.2022045},
author = {Zou, S and Lu, S and Xu, B}
}



@article{AO2017dnn,
doi = {10.1088/1361-6420/aa9581},
url = {https://dx.doi.org/10.1088/1361-6420/aa9581},
year = {2017},
publisher = {IOP Publishing},
volume = {33},
number = {12},
pages = {124007},
author = {Adler, J and \"{O}ktem, O},
title = {Solving ill-posed inverse problems using iterative deep neural networks},
journal = {Inverse Problems}
}


@article{BYZZ2020dnn,
doi = {10.1088/1361-6420/abb447},
url = {https://dx.doi.org/10.1088/1361-6420/abb447},
year = {2020},
publisher = {IOP Publishing},
volume = {36},
number = {11},
pages = {115003},
author = {Bao, G and Ye, X and Zang, Y and Zhou, H},
title = {Numerical solution of inverse problems by weak adversarial networks},
journal = {Inverse Problems}
}

@article{Hoop2016dbar,
doi = {10.1088/0266-5611/32/2/025003},
url = {https://dx.doi.org/10.1088/0266-5611/32/2/025003},
year = {2016},
publisher = {IOP Publishing},
volume = {32},
number = {2},
pages = {025003},
author = {de Hoop, M V and Lassas, M and Santacesaria, M and Siltanen, S and Tamminen, J P},
title = {Positive-energy D-bar method for acoustic tomography: a computational study},
journal = {Inverse Problems}
}

@article {DKSU09,
    AUTHOR = {Dos Santos Ferreira, David and Kenig, Carlos E. and Sj\"{o}strand,
              Johannes and Uhlmann, Gunther},
     TITLE = {On the linearized local {C}alder\'{o}n problem},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {16},
      YEAR = {2009},
    NUMBER = {6},
     PAGES = {955--970},
      ISSN = {1073-2780},
       DOI = {10.4310/MRL.2009.v16.n6.a4},
       URL = {https://doi.org/10.4310/MRL.2009.v16.n6.a4},
}


@article{DS1994,
author = {Dobson, D C and Santosa, F},
title = {Resolution and Stability Analysis of an Inverse Problem in Electrical Impedance Tomography: Dependence on the Input Current Patterns},
journal = {SIAM Journal on Applied Mathematics},
volume = {54},
number = {6},
pages = {1542-1560},
year = {1994},
doi = {10.1137/S0036139992237596},
URL = {https://doi.org/10.1137/S0036139992237596}
}

@article {FY2022,
    AUTHOR = {Fan, Yuwei and Ying, Lexing},
     TITLE = {Solving inverse wave scattering with deep learning},
   JOURNAL = {Ann. Math. Sci. Appl.},
  FJOURNAL = {Annals of Mathematical Sciences and Applications},
    VOLUME = {7},
      YEAR = {2022},
    NUMBER = {1},
     PAGES = {23--48},
      ISSN = {2380-288X},
       DOI = {10.4310/AMSA.2022.v7.n1.a2},
       URL = {https://doi.org/10.4310/AMSA.2022.v7.n1.a2},
}

@article{FY2020,
title = {Solving electrical impedance tomography with deep learning},
journal = {Journal of Computational Physics},
volume = {404},
pages = {109119},
year = {2020},
issn = {0021-9991},
doi = {10.1016/j.jcp.2019.109119},
url = {https://www.sciencedirect.com/science/article/pii/S0021999119308241},
author = {Fan, Y and Ying, L}
}

@article {FanBCR,
    AUTHOR = {Fan, Yuwei and Orozco Bohorquez, Cindy and Ying, Lexing},
     TITLE = {B{CR}-{N}et: a neural network based on the nonstandard wavelet
              form},
   JOURNAL = {J. Comput. Phys.},
  FJOURNAL = {Journal of Computational Physics},
    VOLUME = {384},
      YEAR = {2019},
     PAGES = {1--15},
      ISSN = {0021-9991},
       DOI = {10.1016/j.jcp.2019.02.002},
       URL = {https://doi.org/10.1016/j.jcp.2019.02.002},
}

@article{Ruland2022ipi,
title = {Runge approximation and stability improvement for a partial data Calder\'on problem for the acoustic Helmholtz equation},
journal = {Inverse Problems and Imaging},
volume = {16},number = {1},pages = {251-281},
year = {2022},
issn = {1930-8337},
doi = {10.3934/ipi.2021049},
url = {https://www.aimsciences.org/article/doi/10.3934/ipi.2021049},
author = {Garc\'ia-Ferrero, M \'{A} and R\"uland, A and Zato\'n, W},
}


@article{077_13164,
	author = {Heck, H and Wang, J-N},
	title = {Optimal stability estimate of the inverse boundary value problem by partial measurements},
	journal = {Rendiconti dell'Istituto di matematica dell'Universit\'a di Trieste},
	volume = {48},
	year = {2016},
	publisher = {EUT Edizioni Universit\'a di Trieste},
	doi = {10.13137/2464-8728/13164},
	url= {http://hdl.handle.net/10077/13164},
    issn = {0049-4704},    
}


@article{HI2004increasing,
doi = {10.1088/0266-5611/20/3/004},
url = {https://dx.doi.org/10.1088/0266-5611/20/3/004},
year = {2004},
volume = {20},
number = {3},
pages = {697},
author = {Hrycak, T and Isakov, V},
title = {Increased stability in the continuation of solutions to the Helmholtz equation},
journal = {Inverse Problems}
}

@article{Isakov2007ipi,
title = {On uniqueness in the inverse conductivity problem with local data},
journal = {Inverse Problems and Imaging},
volume = {1},number = {1},pages = {95-105},
year = {2007},
issn = {1930-8337},
doi = {10.3934/ipi.2007.1.95},
url = {https://www.aimsciences.org/article/doi/10.3934/ipi.2007.1.95},
author = {Isakov, V}
}

@article{ILW2016,
author = {Isakov, V and Lai, R-Y and Wang, J-N},
title = {Increasing Stability for the Conductivity and Attenuation Coefficients},
journal = {SIAM Journal on Mathematical Analysis},
volume = {48},
number = {1},
pages = {569-594},
year = {2016},
doi = {10.1137/15M1019052},
URL = {https://doi.org/10.1137/15M1019052}
}


@article{IW2014ipi,
title = {Increasing stability for determining the potential in the Schr\"odinger equation with attenuation from the Dirichlet-to-Neumann map},
journal = {Inverse Problems and Imaging},
volume = {8},number = {4},pages = {1139-1150},
year = {2014},
issn = {1930-8337},
doi = {10.3934/ipi.2014.8.1139},
url = {https://www.aimsciences.org/article/doi/10.3934/ipi.2014.8.1139},
author = {Isakov, V and Wang, J-N}
}


@article{jin2017deep,
  title={Deep convolutional neural network for inverse problems in imaging},
  author={Jin, K H and McCann, M T and Froustey, E and Unser, M},
  journal={IEEE Transactions on Image Processing},
  volume={26},
  number={9},
  pages={4509--4522},
  year={2017},
  publisher={IEEE},
  doi = {10.1109/TIP.2017.2713099},
  url={https://ieeexplore.ieee.org/document/7949028}
}

@article{KU2018,
author = {Krupchyk, K and Uhlmann, G},
title = {Inverse problems for advection diffusion equations in admissible geometries},
journal = {Communications in Partial Differential Equations},
volume = {43},
number = {4},
pages = {585-615},
year  = {2018},
publisher = {Taylor \& Francis},
doi = {10.1080/03605302.2018.1446163},
URL = {https://doi.org/10.1080/03605302.2018.1446163
}
}

@Article{AL2019ai,
AUTHOR = {Khan, T A and Ling, S H},
TITLE = {Review on Electrical Impedance Tomography: Artificial Intelligence Methods and its Applications},
JOURNAL = {Algorithms},
VOLUME = {12},
YEAR = {2019},
NUMBER = {5},
ARTICLE-NUMBER = {88},
URL = {https://www.mdpi.com/1999-4893/12/5/88},
ISSN = {1999-4893},
DOI = {10.3390/a12050088}
}


@article{Li2020,
doi = {10.1088/1361-6420/ab6d57},
url = {https://dx.doi.org/10.1088/1361-6420/ab6d57},
year = {2020},
publisher = {IOP Publishing},
volume = {36},
number = {6},
pages = {065005},
author = {Li, H and Schwab, J and Antholzer, S and Haltmeier, M},
title = {NETT: solving inverse problems with deep neural networks},
journal = {Inverse Problems}
}

@article{Liang2015ipi,
title = {Increasing stability for the inverse problem of the Schr\"odinger equation with the partial Cauchy data},
journal = {Inverse Problems and Imaging},
volume = {9},number = {2},pages = {469-478},
year = {2015},
issn = {1930-8337},
doi = {10.3934/ipi.2015.9.469},
url = {https://www.aimsciences.org/article/doi/10.3934/ipi.2015.9.469},
author = {Liang, L}
}

@book {Du2015,
    AUTHOR = {Duffy, Dean G.},
     TITLE = {Green's functions with applications},
    SERIES = {Studies in Advanced Mathematics},
 PUBLISHER = {Chapman \& Hall/CRC, Boca Raton, FL},
      YEAR = {2001},
      ISBN = {1-58488-110-0},
       DOI = {10.1201/9781420034790},
       URL = {https://doi.org/10.1201/9781420034790},
}

@article{Liu2020ipi,
title = {Stability estimates in a partial data inverse boundary value problem for biharmonic operators at high frequencies},
journal = {Inverse Problems and Imaging},
volume = {14},number = {5},pages = {783-796},
year = {2020},
issn = {1930-8337},
doi = {10.3934/ipi.2020036},
url = {https://www.aimsciences.org/article/doi/10.3934/ipi.2020036},
author = {Liu, B}
}

@article{SU1987,
 ISSN = {0003486X},
 URL = {http://www.jstor.org/stable/1971291},
 author = {Sylvester, J and Uhlmann, G},
 journal = {Annals of Mathematics},
 number = {1},
 pages = {153--169},
 publisher = {Annals of Mathematics},
 title = {A Global Uniqueness Theorem for an Inverse Boundary Value Problem},
 urldate = {2022-12-13},
 volume = {125},
 year = {1987}
}

@article {ZLX1,
    AUTHOR = {Zou, Sen and Lu, Shuai and Xu, Boxi},
     TITLE = {Linearized inverse {S}chr\"{o}dinger potential problem with
              partial data and its deep neural network inversion},
   JOURNAL = {Inverse Probl. Imaging},
  FJOURNAL = {Inverse Problems and Imaging},
    VOLUME = {16},
      YEAR = {2022},
    NUMBER = {6},
     PAGES = {1669--1690},
      ISSN = {1930-8337},
       DOI = {10.3934/ipi.2022045},
       URL = {https://doi.org/10.3934/ipi.2022045},
}

@misc{LZ23,
  doi = {10.48550/ARXIV.2301.07875},
  url = {https://arxiv.org/abs/2301.07875},
  author = {Lu, Shuai and Zhai, Jian},
  title = {Increasing stability of a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds},
  publisher = {arXiv},
  year = {2023},
}

@misc{ZLX2,
  doi = {10.48550/ARXIV.2211.13562},
  url = {https://arxiv.org/abs/2211.13562},
  author = {Zou, Sen and Lu, Shuai and Xu, Boxi},
  title = {Increasing stability of the first order linearized inverse Schrödinger potential problem with integer power type nonlinearities},
  publisher = {arXiv},
  year = {2022},
}


@article {Sun96,
    AUTHOR = {Sun, Ziqi},
     TITLE = {On a quasilinear inverse boundary value problem},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {221},
      YEAR = {1996},
    NUMBER = {2},
     PAGES = {293--305},
      ISSN = {0025-5874},
       DOI = {10.1007/BF02622117},
       URL = {https://doi.org/10.1007/BF02622117},
}

@article {KLU18,
    AUTHOR = {Kurylev, Yaroslav and Lassas, Matti and Uhlmann, Gunther},
     TITLE = {Inverse problems for {L}orentzian manifolds and non-linear
              hyperbolic equations},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {212},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {781--857},
      ISSN = {0020-9910},
       DOI = {10.1007/s00222-017-0780-y},
       URL = {https://doi.org/10.1007/s00222-017-0780-y},
}


@misc{LUW17,
  doi = {10.48550/ARXIV.1703.10704},
  url = {https://arxiv.org/abs/1703.10704},
  author = {Lassas, Matti and Uhlmann, Gunther and Wang, Yiran},
  title = {Determination of vacuum space-times from the Einstein-Maxwell equations},
  publisher = {arXiv},
  year = {2017},
}


@article {LUW18,
    AUTHOR = {Lassas, Matti and Uhlmann, Gunther and Wang, Yiran},
     TITLE = {Inverse problems for semilinear wave equations on {L}orentzian
              manifolds},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {360},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {555--609},
      ISSN = {0010-3616},
       DOI = {10.1007/s00220-018-3135-7},
       URL = {https://doi.org/10.1007/s00220-018-3135-7},
}


