STABILITY FOR DETERMINATION OF RIEMANNIAN METRICS BY SPECTRAL DATA AND DIRICHLET-TO-NEUMANN MAP LIMITED ON ARBITRARY SUBBOUNDARY

被引：1

作者：

Imanuvilov, Oleg Yu ^{[1
]}

Yamamoto, Masahiro ^{[2
,3
,4
]}

机构：

[1] Colorado State Univ, Dept Math, 101 Weber Bldg, Ft Collins, CO 80523 USA

[2] Univ Tokyo, Dept Math Sci, Meguro Ku, Tokyo 153, Japan

[3] Acad Romanian Scientists, Splaiul Independentei St 54, Bucharest 050094, Romania

[4] Peoples Friendship Univ Russia, RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia

来源：

INVERSE PROBLEMS AND IMAGING | 2019年 / 13卷 / 06期

基金：

中国国家自然科学基金; 日本学术振兴会;

关键词：

Spectral data; Dirichlet-to-Neumann map; stability; CALDERON INVERSE PROBLEM; BORG-LEVINSON THEOREM; WAVE-EQUATION; RECONSTRUCTION; UNIQUENESS;

D O I：

10.3934/ipi.2019054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish conditional stability estimates for two inverse problems of determining metrics in two dimensional Laplace-Beltrami operators. As data, in the first inverse problem we adopt spectral data on an arbitrarily fixed subboundary, while in the second, we choose the Dirichlet-to-Neumann map limited on an arbitrarily fixed subboundary. The conditional stability estimates for the two inverse problems are stated as follows. If the difference between spectral data or Dirichlet-to-Neumann maps related to two metrics g(1) and g(2) is small, then g(1) and g(2) are close in L-2(Omega) modulo a suitable diffeomorphism within a priori bounds of g(1) and g(2). Both stability estimates are of the same double logarithmic rate.

引用

页码：1213 / 1258

页数：46

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