Regularity of solutions to time-harmonic Maxwell's system with H\"older and various lower than H\"older continuous coefficients

TL;DR

This paper develops a Schauder theory for the time-harmonic Maxwell's system, proving global H"older regularity of solutions with coefficients that are H"older continuous or less regular.

Contribution

It establishes the first comprehensive Schauder regularity results for Maxwell's equations with coefficients of varying regularity, including those less than H"older continuous.

Findings

Proved global H"older regularity for solutions with H"older continuous coefficients.

Extended regularity results to coefficients with lower than H"older continuity.

Raised the H"older index to the interval (0,1) for solutions.

Abstract

The purpose of this paper is to establish a complete Schauder theory for the second-order linear elliptic equation and the time-harmonic Maxwell's system. We prove global H\"older regularity for the solutions to the time-harmonic anisotropic Maxwell's equations under H\"older continuous coefficients, raising the H\"older index to the interval (0,1)