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.
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页码：679 / 699
页数：21
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