An epsilon-regularity result for Griffith almost-minimizers in the plane
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914034222104576 |
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| author | Friedrich, Manuel Labourie, Camille Stinson, Kerrek |
| author_facet | Friedrich, Manuel Labourie, Camille Stinson, Kerrek |
| contents | We present regularity results for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we prove an epsilon-regularity theorem showing that the crack is locally a $C^{1,1/2}$ curve outside of a singular set of zero Hausdorff measure. The main novelty is that, in contrast to previous results, no topological constraints on the crack are required. The results also apply to almost-minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07670 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An epsilon-regularity result for Griffith almost-minimizers in the plane Friedrich, Manuel Labourie, Camille Stinson, Kerrek Analysis of PDEs 49J45, 70G75, 74B20, 74G65, 74R10, 74A30 We present regularity results for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we prove an epsilon-regularity theorem showing that the crack is locally a $C^{1,1/2}$ curve outside of a singular set of zero Hausdorff measure. The main novelty is that, in contrast to previous results, no topological constraints on the crack are required. The results also apply to almost-minimizers. |
| title | An epsilon-regularity result for Griffith almost-minimizers in the plane |
| topic | Analysis of PDEs 49J45, 70G75, 74B20, 74G65, 74R10, 74A30 |
| url | https://arxiv.org/abs/2310.07670 |