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

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 $H^1(\Omega)$.