Inverse Boundary Value Problem for Maxwell Equations with Local Data

被引：41

作者：

Caro, Pedro ^{[2
]}

Ola, Petri ^{[1
]}

Salo, Mikko ^{[1
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland

[2] Univ Autonoma Madrid, Dept Math, Madrid, Spain

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 34卷 / 11期

基金：

芬兰科学院;

关键词：

Inverse problem; Maxwell equations; Partial data; MATERIAL PARAMETERS; UNIQUENESS; INFORMATION;

D O I：

10.1080/03605300903296272

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the boundary. We assume that the inaccessible part of the boundary is either part of a plane, or part of a sphere. This work generalizes the results obtained by Isakov [4] for the Schrodinger equation to Maxwell equations.

引用

页码：1425 / 1464

页数：40

共 19 条

[1] Recovering a potential from partial Cauchy data [J].

Bukhgeim, AL ;

Uhlmann, G .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2002, 27 (3-4) :653-668

[2]

CALDER\ON A. P., 1980, SEMINAR NUMERICAL AN, P65, DOI DOI 10.1590/S0101-82052006000200002

[3] THE UNIQUENESS OF A SOLUTION TO AN INVERSE SCATTERING PROBLEM FOR ELECTROMAGNETIC-WAVES [J].

COLTON, D ;

PAIVARINTA, L .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1992, 119 (01) :59-70

[4] On uniqueness in the inverse conductivity problem with local data [J].

Isakov, Victor .

INVERSE PROBLEMS AND IMAGING, 2007, 1 (01) :95-105

[5] Total determination of material parameters from electromagnetic boundary information [J].

Joshi, MS ;

McDowall, SR .

PACIFIC JOURNAL OF MATHEMATICS, 2000, 193 (01) :107-129

[6] The Calderon problem with partial data [J].

Kenig, Carlos E. ;

Sjostrand, Johannes ;

Uhlmann, Gunther .

ANNALS OF MATHEMATICS, 2007, 165 (02) :567-591

[7]

KENIG CE, ARXIV09053275

[8] Boundary determination of material parameters from electromagnetic boundary information [J].

McDowall, SR .

INVERSE PROBLEMS, 1997, 13 (01) :153-163

[9] An electromagnetic inverse problem in chiral media [J].

McDowall, SR .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (07) :2993-3013

[10] Finite energy solutions of Maxwell's equations and constructive Hodge decompositions on nonsmooth Riemannian manifolds [J].

Mitrea, D ;

Mitrea, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 190 (02) :339-417

← 1 2 →