Uniqueness for the inverse boundary value problem with singular potentials in 2D

被引：6

作者：

Blasten, Emilia ^{[1
,2
]}

Tzou, Leo ^{[3
]}

Wang, Jenn-Nan ^{[4
]}

机构：

[1] HKUST Jockey Club Inst Adv Study, Clear Water Bay, Hong Kong, Peoples R China

[2] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

[3] Univ Sydney, Fac Sci, Sydney, NSW, Australia

[4] Natl Taiwan Univ, NCTS, Inst Appl Math Sci, Taipei 106, Taiwan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2020年 / 295卷 / 3-4期

基金：

澳大利亚研究理事会;

关键词：

CONDUCTIVITY PROBLEM; CAUCHY DATA;

D O I：

10.1007/s00209-019-02436-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the inverse boundary value problem for the Schrodinger equation with potential in Lp. We show that the potential is uniquely determined by the boundary measurements.

引用

页码：1521 / 1535

页数：15

共 24 条

[1] LP-INEQUALITIES FOR THE LAPLACIAN AND UNIQUE CONTINUATION [J].

AMREIN, WO ;

BERTHIER, AM ;

GEORGESCU, V .

ANNALES DE L INSTITUT FOURIER, 1981, 31 (03) :153-168

[2]

Astala K., 2009, PRINCETON MATH SERIE, V48

[3] Calderon's inverse conductivity problem in the plane [J].

Astala, Kari ;

Paivarinta, Lassi .

ANNALS OF MATHEMATICS, 2006, 163 (01) :265-299

[4]

BLASTEN E., 2013, THESIS

[5] STABILITY AND UNIQUENESS FOR A TWO-DIMENSIONAL INVERSE BOUNDARY VALUE PROBLEM FOR LESS REGULAR POTENTIALS [J].

Blasten, Eemeli ;

Imanuvilov, Oleg Yu. ;

Yamamoto, Masahiro .

INVERSE PROBLEMS AND IMAGING, 2015, 9 (03) :709-723

[6] Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions [J].

Brown, RM ;

Uhlmann, GA .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1997, 22 (5-6) :1009-1027

[7] Recovering a potential from Cauchy data in the two-dimensional case [J].

Bukhgeim, A. L. .

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2008, 16 (01) :19-33

[8]

Cârstea CI, 2018, ANN SCUOLA NORM-SCI, V18, P1459

[9] Determining an Unbounded Potential from Cauchy Data in Admissible Geometries [J].

Ferreira, David Dos Santos ;

Kenig, Carlos E. ;

Salo, Mikko .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2013, 38 (01) :50-68

[10] Unique Determination of a Magnetic Schrodinger Operator with Unbounded Magnetic Potential from Boundary Data [J].

Haberman, Boaz .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2018, 2018 (04) :1080-1128

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