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...

Full description

Saved in:
Bibliographic Details
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
Subjects:
35Q60
35R30
Inverse problems
PDEs in connection with optics and electromagnetic theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-1272903