H\"older regularity for Maxwell's equations under minimal assumptions on the coefficients

TL;DR

This paper establishes global H"older regularity for solutions to time-harmonic anisotropic Maxwell's equations with minimal assumptions on the coefficients, including cases with bianisotropic materials.

Contribution

It proves the regularity results under the weakest coefficient assumptions to date, extending the theory to more general anisotropic and bianisotropic materials.

Findings

Global H"older regularity proven for solutions

Regularity holds with minimal coefficient assumptions

Estimates valid for bianisotropic parameters

Abstract

We prove global H\"older regularity for the solutions to the time-harmonic anisotropic Maxwell's equations, under the assumptions of H\"older continuous coefficients. The regularity hypotheses on the coefficients are minimal. The same estimates hold also in the case of bianisotropic material parameters.