Korn's inequality in anisotropic Sobolev spaces
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916912350363648 |
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| author | Benavides, Gonzalo A. Domínguez-Rivera, Sebastián A. |
| author_facet | Benavides, Gonzalo A. Domínguez-Rivera, Sebastián A. |
| contents | Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large variety of problems in continuum mechanics. In this paper, we prove that the classical Korn inequality holds true in {\it anisotropic Sobolev spaces}. We also prove that an extension of Korn's inequality, involving non-linear continuous maps, is valid in such spaces. Finally, we point out that another classical inequality, Poincare's inequality, also holds in anisotropic Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00874 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Korn's inequality in anisotropic Sobolev spaces Benavides, Gonzalo A. Domínguez-Rivera, Sebastián A. Analysis of PDEs Functional Analysis 26D10, 35A23, 74B05, 74B20 Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large variety of problems in continuum mechanics. In this paper, we prove that the classical Korn inequality holds true in {\it anisotropic Sobolev spaces}. We also prove that an extension of Korn's inequality, involving non-linear continuous maps, is valid in such spaces. Finally, we point out that another classical inequality, Poincare's inequality, also holds in anisotropic Sobolev spaces. |
| title | Korn's inequality in anisotropic Sobolev spaces |
| topic | Analysis of PDEs Functional Analysis 26D10, 35A23, 74B05, 74B20 |
| url | https://arxiv.org/abs/2212.00874 |