NON-UNIQUENESS RESULTS FOR THE ANISOTROPIC CALDERON PROBLEM WITH DATA MEASURED ON DISJOINT SETS

被引：12
作者：
Daude, Thierry [1 ]
Kamran, Niky [2 ]
Nicoleau, Francois [3 ]
机构：
[1] Univ Cergy Pontoise, Dept Math, UMR CNRS 8088, F-95302 Cergy Pontoise, France
[2] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada
[3] Francois NICOLEAU, Lab Math Jean Leray, UMR CNRS 6629, 2 Rue Houssiniere BP 92208, F-44322 Nantes 03, France
来源：
ANNALES DE L INSTITUT FOURIER | 2019年 / 69卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Anisotropic Calderon problem; Helmholtz equation on a Riemannian manifold; Sturm-Liouville problems; Weyl-Titchmarsh functions; INVERSE PROBLEMS; FIXED-ENERGY; UNIQUENESS; CONDUCTIVITY; SCATTERING; MANIFOLDS; OPERATORS;
D O I：
10.5802/aif.3240
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we show that there is non-uniqueness in the Calderon problem on Riemannian manifolds when the Dirichlet and Neumann data are measured on disjoint sets of the boundary. We provide counterexamples in the case of two and three dimensional Riemannian manifolds with boundary having the topology of circular cylinders in dimension two and toric cylinders in dimension three. The construction could be easily extended to higher dimensional Riemannian manifolds.
引用
收藏
页码：119 / 170
页数：52
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