An anisotropic inverse boundary value problem. (English) Zbl 0709.35102

The impedance tomography problem for anisotropic conductivities is under consideration. It is well known that the solution is not unique (different from the isotropic problem): for a bounded region \(\Omega\) in space any diffeomorphism of \(\Omega\) which fixes the boundary can be used to construct a new conductivity with the same voltage to current map on \(\partial \Omega\). The main result proved in this paper is that: for any two 2-dimensional conductivity distributions \(\gamma_ 1\) and \(\gamma_ 2\) which produce the same boundary measurements and which are “near a constant”, there exists a certain diffeomorphism \(\Psi\) such that \(\Psi_*\gamma_ 2=\gamma_ 1\).
Reviewer: H.Ding


35R30 Inverse problems for PDEs
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
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