A global higher regularity result for the static relaxed micromorphic model on smooth domains

TL;DR

This paper establishes a global higher regularity result for solutions of the linear relaxed micromorphic model, which couples elliptic PDEs with Maxwell-type systems, on smooth domains.

Contribution

It provides a new regularity result for the coupled micromorphic and Maxwell-type PDE system using Helmholtz decomposition and elliptic regularity techniques.

Findings

Achieves higher regularity for weak solutions on smooth domains.

Combines Helmholtz decomposition with elliptic regularity results.

Extends understanding of the mathematical properties of the relaxed micromorphic model.

Abstract

We derive a global higher regularity result for weak solutions of the linear relaxed micromorphic model on smooth domains. The governing equations consist of a linear elliptic system of partial differential equations that is coupled with a system of Maxwell-type. The result is obtained by combining a Helmholtz decomposition argument with regularity results for linear elliptic systems and the classical embedding of $H(\mathrm{div};\Omega)\cap H_0(\mathrm{curl};\Omega)$ into $H^1(\Omega)$.