LIPSCHITZ STABILITY OF AN INVERSE BOUNDARY VALUE PROBLEM FOR A SCHRODINGER-TYPE EQUATION

被引：43

作者：

Beretta, Elena ^{[1
]}

de Hoop, Maarten V. ^{[2
]}

Qiu, Lingyun ^{[2
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat Guido Castelnuovo, Rome, Italy

[2] Purdue Univ, Ctr Computat & Appl Math, W Lafayette, IN 47907 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 02期

基金：

美国国家科学基金会;

关键词：

Lipschitz stability; Schrodinger equation; Helmholtz equation; inverse boundary value problem;

D O I：

10.1137/120869201

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the inverse boundary value problem of determining the potential in the Schrodinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that, under general settings, the optimal stability estimate is of logarithmic type. In this work, a Lipschitz-type stability is established assuming a priori that the potential is piecewise constant with a bounded known number of unknown values.

引用

页码：679 / 699

页数：21

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