Inverse problems for the anisotropic Maxwell equations

TL;DR

This paper establishes unique determination of anisotropic electromagnetic parameters from boundary data in Maxwell equations, using advanced Fourier analysis and complex geometrical optics solutions on specific manifolds.

Contribution

It introduces a new Fourier analytic approach to prove uniqueness in inverse boundary value problems for anisotropic Maxwell equations on admissible manifolds.

Findings

Unique boundary determination of anisotropic parameters in Maxwell equations.

Development of Fourier analytic methods for complex geometrical optics solutions.

Applicability to both Riemannian manifolds and Euclidean space with admissible coefficients.

Abstract

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.