Carleman estimate for the Schrodinger equation and application to magnetic inverse problems

被引：11

作者：

Huang, Xinchi ^{[1
]}

Kian, Yavar ^{[2
]}

Soccorsi, Eric ^{[2
]}

Yamamoto, Masahiro ^{[1
,3
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 153, Japan

[2] Univ Toulon & Var, Aix Marseille Univ, CNRS, CPT, Marseille, France

[3] RUDN Univ, Peoples Friendship Univ Russia, 6 Miklukho Maklaya St, Moscow 117198, Russia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 474卷 / 01期

基金：

日本学术振兴会;

关键词：

Multidimensional inverse coefficient problem; Magnetic Schrodinger equation; Carleman estimate; STABLE DETERMINATION; STABILITY; POTENTIALS; UNIQUENESS; OPERATORS;

D O I：

10.1016/j.jmaa.2019.01.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove Lipschitz stable determination of the complex-valued electric potential and the direction of the magnetic field appearing in the dynamic Schrodinger equation with static coefficients, by finitely many partial boundary measurements of the solution. This is by means of the Bukhgeim-Klibanov method, based on an appropriate Carleman estimate. Since the time symmetrization of the static magnetic Schrodinger equation around t = 0 is not possible, we preliminarily establish a Carleman inequality specifically designed for this problem. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：116 / 142

页数：27

共 35 条

[1]

Albano P., 2000, Electronic Journal of Differential Equations, V2000, P1

[2] Uniqueness and stability in an inverse problem for the Schrodinger equation [J].

Baudouin, L ;

Puel, JP .

INVERSE PROBLEMS, 2002, 18 (06) :1537-1554

[3] An inverse stability result for non-compactly supported potentials by one arbitrary lateral Neumann observation [J].

Bellassoued, M. ;

Kian, Y. ;

Soccorsi, E. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (10) :7535-7562

[4] Inverse boundary value problem for the dynamical heterogeneous Maxwell's system [J].

Bellassoued, Mourad ;

Cristofol, Michel ;

Soccorsi, Eric .

INVERSE PROBLEMS, 2012, 28 (09)

[5] Stability estimate for an inverse problem for the magnetic Schrodinger equation from the Dirichlet-to-Neumann map [J].

Bellassoued, Mourad ;

Choulli, Mourad .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 258 (01) :161-195

[6] Logarithmic stability in the dynamical inverse problem for the Schrodinger equation by arbitrary boundary observation [J].

Bellassoued, Mourad ;

Choulli, Mourad .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2009, 91 (03) :233-255

[7] Simultaneous determination of the magnetic field and the electric potential in the Schrodinger equation by a finite number of boundary observations [J].

Ben Aicha, Ibtissem ;

Mejri, Youssef .

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2018, 26 (02) :201-209

[8] A stability estimate for an inverse problem for the Schrodinger equation in a magnetic field from partial boundary measurements [J].

Ben Joud, Hajer .

INVERSE PROBLEMS, 2009, 25 (04)

[9]

Bukhgeim AL., 1981, Sov. Math. Dokl, V24, P244

[10] STABLE DETERMINATION OF TIME-DEPENDENT SCALAR POTENTIAL FROM BOUNDARY MEASUREMENTS IN A PERIODIC QUANTUM WAVEGUIDE [J].

Choulli, Mourad ;

Kian, Yavar ;

Soccorsi, Eric .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (06) :4536-4558

← 1 2 3 4 →