Non-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets

2015/10/22 by Thierry Daudé, Niky Kamran, Daudé, Thierry +3 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.1510.06559

arxiv created 2015/10/22 · arxiv updated 2015/10/23

Abstract

In this paper, we give some simple counterexamples to uniqueness for the Calderon problem on Riemannian manifolds with boundary 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.

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• Inverse scattering at fixed energy on three-dimensional asymptotically hyperbolic Stäckel manifolds
• On the hidden mechanism behind non-uniqueness for the anisotropic Calderón problem with data on disjoint sets

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