Inverse boundary value problem for Maxwell equations with local data

TL;DR

This paper establishes a uniqueness theorem for an inverse boundary value problem related to Maxwell equations, where boundary data is only partially known, extending prior results from Schrödinger equations to electromagnetic systems.

Contribution

It generalizes existing inverse boundary value problem results to Maxwell equations with partial boundary data, including specific geometric boundary conditions.

Findings

Proves uniqueness for Maxwell inverse problems with partial boundary data.

Extends Isakov's results from Schrödinger to Maxwell equations.

Addresses cases with boundary parts as planes or spheres.

Abstract

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or part of a sphere. This work generalizes the results obtained by Isakov for the Schr\"odinger equation to Maxwell equations.