An inverse problem for Maxwell's equations with Lipschitz parameters

TL;DR

This paper proves that the electromagnetic properties of a body, modeled as Lipschitz continuous parameters, can be uniquely determined from boundary measurements of electric and magnetic fields at a fixed frequency.

Contribution

It establishes a uniqueness result for an inverse boundary value problem for Maxwell's equations with Lipschitz continuous parameters.

Findings

Lipschitz continuous parameters are uniquely recoverable from boundary data.

Boundary measurements of tangential electric and magnetic fields suffice for unique identification.

The result applies at a fixed frequency, simplifying practical measurement requirements.

Abstract

We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric permittivity, and magnetic permeability are uniquely determined by knowledge of all tangential electric and magnetic fields on the boundary of the body at a fixed frequency.