A global higher regularity result for the static relaxed micromorphic model on smooth domains
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911521254146048 |
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| author | Knees, Dorothee Owczarek, Sebastian Neff, Patrizio |
| author_facet | Knees, Dorothee Owczarek, Sebastian Neff, Patrizio |
| contents | 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 $H(\mathrm{div};Ω)\cap H_0(\mathrm{curl};Ω)$ into $H^1(Ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02621 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A global higher regularity result for the static relaxed micromorphic model on smooth domains Knees, Dorothee Owczarek, Sebastian Neff, Patrizio Analysis of PDEs 35Q74, 35B65, 49N60, 74A35, 74G40 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 $H(\mathrm{div};Ω)\cap H_0(\mathrm{curl};Ω)$ into $H^1(Ω)$. |
| title | A global higher regularity result for the static relaxed micromorphic model on smooth domains |
| topic | Analysis of PDEs 35Q74, 35B65, 49N60, 74A35, 74G40 |
| url | https://arxiv.org/abs/2307.02621 |