A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929617634328576 |
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| author | Botti, Michele Mascotto, Lorenzo |
| author_facet | Botti, Michele Mascotto, Lorenzo |
| contents | We prove a Nečas-Lions inequality with symmetric gradients on two and three dimensional domains of diameter $R$ that are star-shaped with respect to a ball of radius $ρ$; the constants in the inequality are explicit with respect to $R$ and $ρ$. Crucial tools in deriving this inequality are a first order Babuška-Aziz inequality based on Bogovskiĭ's construction of a right-inverse of the divergence and Fourier transform techniques proposed by Durán. As a byproduct, we derive arbitrary order estimates in arbitrary dimension for that operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality Botti, Michele Mascotto, Lorenzo Analysis of PDEs 35C05, 35C15, 35S05, 42B20, 42B37, 53A45 We prove a Nečas-Lions inequality with symmetric gradients on two and three dimensional domains of diameter $R$ that are star-shaped with respect to a ball of radius $ρ$; the constants in the inequality are explicit with respect to $R$ and $ρ$. Crucial tools in deriving this inequality are a first order Babuška-Aziz inequality based on Bogovskiĭ's construction of a right-inverse of the divergence and Fourier transform techniques proposed by Durán. As a byproduct, we derive arbitrary order estimates in arbitrary dimension for that operator. |
| title | A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality |
| topic | Analysis of PDEs 35C05, 35C15, 35S05, 42B20, 42B37, 53A45 |
| url | https://arxiv.org/abs/2408.00371 |