Korn's inequality from the viewpoint of calculus of variations
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914414816395264 |
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| author | Cassese, Gabriele |
| author_facet | Cassese, Gabriele |
| contents | We study the best possible constants in Korn-type inequalities and their connection with Morrey's problem in the calculus of variations. We adapt techniques from the analysis of the Beurling-Ahlfors transform to Korn's inequality. In particular we show that the constant in Korn's inequality admits a dimension-free bound, and we obtain an estimate that is sharp up to a factor of $\sqrt 3$. In the radial case, the estimate is sharp. We also establish several improvements to estimates in various function spaces. Using a weighted version of Burkholder's differential subordination theorem, recently introduced in [J. Reine Angew. Math. 824 (2025), pp. 137-166],we also prove a dimension-free weighted version of the inequality for Muckenhoupt weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Korn's inequality from the viewpoint of calculus of variations Cassese, Gabriele Analysis of PDEs 35A23, 49J45 (Primary) 26D10(Secondary) We study the best possible constants in Korn-type inequalities and their connection with Morrey's problem in the calculus of variations. We adapt techniques from the analysis of the Beurling-Ahlfors transform to Korn's inequality. In particular we show that the constant in Korn's inequality admits a dimension-free bound, and we obtain an estimate that is sharp up to a factor of $\sqrt 3$. In the radial case, the estimate is sharp. We also establish several improvements to estimates in various function spaces. Using a weighted version of Burkholder's differential subordination theorem, recently introduced in [J. Reine Angew. Math. 824 (2025), pp. 137-166],we also prove a dimension-free weighted version of the inequality for Muckenhoupt weights. |
| title | Korn's inequality from the viewpoint of calculus of variations |
| topic | Analysis of PDEs 35A23, 49J45 (Primary) 26D10(Secondary) |
| url | https://arxiv.org/abs/2603.22431 |