Determining a first order perturbation of the biharmonic operator by partial boundary measurements

被引：50

作者：

Krupchyk, Katsiaryna ^{[2
]}

Lassas, Matti ^{[2
]}

Uhlmann, Gunther ^{[1
,3
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland

[3] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 04期

基金：

芬兰科学院; 美国国家科学基金会;

关键词：

Inverse problem; Biharmonic; Partial data; INVERSE CONDUCTIVITY PROBLEM; PARTIAL CAUCHY DATA; GLOBAL UNIQUENESS; CALDERON PROBLEM; SCHRODINGER-EQUATION; MAGNETIC-FIELD; NEUMANN MAP; LOCAL DATA; RECONSTRUCTION; INVISIBILITY;

D O I：

10.1016/j.jfa.2011.11.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider an operator Delta(2) + A(x) . D+q(x) with the Navier boundary conditions on a bounded domain in R-n, n >= 3. We show that a first order perturbation A(x) . D+q can be determined uniquely by measuring the Dirichlet-to-Neumann map on possibly very small subsets of the boundary of the domain. Notice that the corresponding result does not hold in general for a first order perturbation of the Laplacian. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1781 / 1801

页数：21

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