An inverse boundary value problem for the Maxwell's equations with partial data

TL;DR

This paper addresses an inverse boundary problem for Maxwell's equations, demonstrating that key electromagnetic properties can be uniquely identified locally under specific geometric conditions.

Contribution

It introduces a new uniqueness result for inverse Maxwell problems with partial boundary data using convex foliation assumptions.

Findings

Unique local determination of permittivity, conductivity, and permeability.

Applicability under geometric conditions involving convex foliation.

Advancement in inverse boundary value problem theory for Maxwell's equations.

Abstract

We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with respect to the wave speed.