Regularity Results for Generalized Electro-Magnetic Problems

TL;DR

This paper establishes boundary regularity results for generalized Maxwell equations on Riemannian manifolds, including exterior domains, using differential forms calculus, enhancing understanding of electromagnetic problems in complex geometries.

Contribution

It introduces new boundary regularity results for generalized Maxwell equations on Riemannian manifolds employing differential forms calculus.

Findings

Regularity results up to the boundary for Maxwell equations on manifolds.

Polynomially weighted regularity in exterior domains.

Analysis of homogeneous and inhomogeneous boundary data.

Abstract

We prove regularity results up to the boundary for time independent generalized Maxwell equations on Riemannian manifolds with boundary using the calculus of alternating differential forms. We discuss homogeneous and inhomogeneous boundary data and show 'polynomially weighted' regularity in exterior domains as well.