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A global higher regularity result for the static relaxed micromorphic model on smooth domains
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 20 May 2024, pp. 1-15
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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 $H(\operatorname {div};\Omega )\cap H_0(\operatorname {curl};\Omega )$
into $H^1(\Omega )$
.
