Boundary determination of electromagnetic parameters from local data

TL;DR

This paper improves the understanding of boundary electromagnetic parameter determination by showing they are uniquely recoverable to infinite order from local data, even with unknown obstacles, using singularity analysis.

Contribution

It extends and simplifies previous methods to prove boundary uniqueness for Maxwell equations using only local Cauchy data, disregarding obstacles.

Findings

Electromagnetic parameters are uniquely determined to infinite order at the boundary.

The method relies on singularity analysis of solutions to Maxwell's equations.

Results hold even in the presence of unknown obstacles.

Abstract

In this paper, we extend and simplify the methods in [13] to improve the results on uniqueness of the boundary determination for the Maxwell equation. In particular, we show that the electromagnetic parameters are uniquely determined to infinite order at the boundary from the local admittance map, disregarding the presence of an unknown obstacle, where actually only the local Cauchy data of the fundamental solution are used. The proof mainly relies on an elaborate singularity analysis on certain singular solutions to the Maxwell equation.