Inverse problems for the anisotropic Maxwell equations

We prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time-harmonic Maxwell equations in certain anisotropic settings. We give a uniqueness result in the inverse problem for Maxwell equations on an admissible Riemannian manifold and a uniquene...

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Published in:Duke mathematical journal 2011-04, Vol.157 (2), p.369-419
Main Authors: Kenig, Carlos E., Salo, Mikko, Uhlmann, Gunther
Format: Article
Language:English
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35Q60
35R30
Inverse problems
PDEs in connection with optics and electromagnetic theory
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description We prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time-harmonic Maxwell equations in certain anisotropic settings. We give a uniqueness result in the inverse problem for Maxwell equations on an admissible Riemannian manifold and a uniqueness result for Maxwell equations in Euclidean space with admissible matrix coefficients. The proofs are based on a new Fourier analytic construction of complex geometrical optics solutions on admissible manifolds and involve a proper notion of uniqueness for such solutions.
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subjects 35Q60
35R30
Inverse problems
PDEs in connection with optics and electromagnetic theory
title Inverse problems for the anisotropic Maxwell equations
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