Inverse boundary value problem for the dynamical heterogeneous Maxwell system

TL;DR

This paper establishes a H"older stability estimate for determining inhomogeneous electromagnetic properties in Maxwell's equations from limited boundary measurements, using a global Carleman estimate.

Contribution

It introduces a novel stability estimate for the inverse boundary value problem in heterogeneous Maxwell's system with partial boundary data.

Findings

Proves a H"older stability estimate for the inverse problem.

Develops a global Carleman estimate for Maxwell's system.

Demonstrates stability with measurements on only some boundary components.

Abstract

We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a H\"older stability estimate for the inverse problem, where the measurements are exerted only in some boundary components. For it, we prove a global Carleman estimate for the heterogeneous Maxwell's system with boundary conditions.