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
收藏
页码：725 / 746
页数：22
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