Geometric properties of free boundaries in degenerate quenching problems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908838258540544 |
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| author | Araújo, Damião J. Teymurazyan, Rafayel Urbano, José Miguel |
| author_facet | Araújo, Damião J. Teymurazyan, Rafayel Urbano, José Miguel |
| contents | We study minimizers of non-differentiable functionals modeled on the degenerate quenching problem. Our main result establishes the finiteness of the $(n-1)-$dimensional Hausdorff measure of the free boundary. The proof is based on optimal gradient decay estimates obtained from an intrinsic Harnack-type inequality, along with a detailed analysis in a flatness regime, where minimizers enjoy improved regularity. Our arguments provide an alternative proof of classical results of Phillips and, although developed in the degenerate setting, also offer insights relevant to the singular case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric properties of free boundaries in degenerate quenching problems Araújo, Damião J. Teymurazyan, Rafayel Urbano, José Miguel Analysis of PDEs We study minimizers of non-differentiable functionals modeled on the degenerate quenching problem. Our main result establishes the finiteness of the $(n-1)-$dimensional Hausdorff measure of the free boundary. The proof is based on optimal gradient decay estimates obtained from an intrinsic Harnack-type inequality, along with a detailed analysis in a flatness regime, where minimizers enjoy improved regularity. Our arguments provide an alternative proof of classical results of Phillips and, although developed in the degenerate setting, also offer insights relevant to the singular case. |
| title | Geometric properties of free boundaries in degenerate quenching problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.11536 |