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arXiv · 2307.02621

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

Dorothee Knees·Sebastian Owczarek·Patrizio Neff
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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 $H^1(\Omega)$.

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Dorothee Knees, Sebastian Owczarek, Patrizio Neff. 2023-07-05. A global higher regularity result for the static relaxed micromorphic model on smooth domains. https://doi.org/10.1017/prm.2024.63

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