Single logarithmic conditional stability in determining unknown boundaries

被引：1

作者：

Elschner, Johannes ^{[1
]}

Hu, Guanghui ^{[2
]}

Yamamoto, Masahiro ^{[3
,4
]}

机构：

[1] Weierstrass Inst, Berlin, Germany

[2] Beijing Computat Sci Res Ctr, Bldg 9,ZPk 2,10 Xibeiwang East Rd, Beijing 100193, Peoples R China

[3] Univ Tokyo, Dept Math Sci, Tokyo, Japan

[4] Peoples Friendship Univ Russia, Ctr Nonlinear Problems Math Phys, Moscow, Russia

来源：

APPLICABLE ANALYSIS | 2020年 / 99卷 / 05期

基金：

日本学术振兴会;

关键词：

Bo Zhang; Conditional stability; elliptic equations; Carleman estimate; inverse scattering; single Cauchy data; INVERSE PROBLEM; STABLE DETERMINATION; LOCAL UNIQUENESS; SOFT OBSTACLES; EQUATION;

D O I：

10.1080/00036811.2018.1508654

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a conditional stability estimate of log-type for determining unknown boundaries from a single Cauchy data taken on an accessible sub-boundary. Our approach relies on new interior and boundary estimates for elliptic equations which are derived from the Carleman estimate. Stability results for target identification of an acoustic sound-soft scatterer from one or several far-field patterns are also obtained.

引用

页码：725 / 746

页数：22

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