A short proof of Allard's and Brakke's regularity theorems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916093792092160 |
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| author | De Philippis, Guido Gasparetto, Carlo Schulze, Felix |
| author_facet | De Philippis, Guido Gasparetto, Carlo Schulze, Felix |
| contents | We give new short proofs of Allard's regularity theorem for varifolds with bounded first variation and Brakke's regularity theorem for integral Brakke flows with bounded forcing. They are based on a decay of flatness, following from weighted versions of the respective monotonicity formulas, together with a characterization of non-homogeneous blow-ups using the viscosity approach introduced by Savin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02490 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A short proof of Allard's and Brakke's regularity theorems De Philippis, Guido Gasparetto, Carlo Schulze, Felix Analysis of PDEs Differential Geometry We give new short proofs of Allard's regularity theorem for varifolds with bounded first variation and Brakke's regularity theorem for integral Brakke flows with bounded forcing. They are based on a decay of flatness, following from weighted versions of the respective monotonicity formulas, together with a characterization of non-homogeneous blow-ups using the viscosity approach introduced by Savin. |
| title | A short proof of Allard's and Brakke's regularity theorems |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2306.02490 |