Uniqueness for an inverse problem in electromagnetism with partial data

TL;DR

This paper proves a uniqueness theorem for recovering electromagnetic coefficients in Maxwell's equations from partial boundary data without special geometric restrictions, assuming coefficients match near the boundary.

Contribution

It establishes a new uniqueness result for inverse electromagnetic problems with minimal geometric assumptions and natural coefficient conditions.

Findings

Uniqueness of coefficient recovery from partial boundary data

No geometric restrictions on inaccessible boundary parts

Coefficients assumed to coincide near boundary

Abstract

A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the boundary of the domain, apart from imposing that the boundary of the domain is $C^{1,1}$. The coefficients are assumed to coincide on a neighbourhood of the boundary, a natural property in applications.