Improved moduli of continuity for degenerate phase transitions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929468025602048 |
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| author | Gianazza, Ugo Liao, Naian Urbano, José Miguel |
| author_facet | Gianazza, Ugo Liao, Naian Urbano, José Miguel |
| contents | We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the $N$-dimensional, two-phase Stefan problem featuring a $p-$degenerate diffusion: for $p=N\geq 3$, we sharpen it to $$ \boldsymbolω(r) \approx \exp (-c| \ln r|^{\frac1N}); $$ for $p>\max\{2,N\}$, we derive an unexpected Hölder modulus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved moduli of continuity for degenerate phase transitions Gianazza, Ugo Liao, Naian Urbano, José Miguel Analysis of PDEs 35K65, 35K92, 35B65, 76S05, 80A22 We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the $N$-dimensional, two-phase Stefan problem featuring a $p-$degenerate diffusion: for $p=N\geq 3$, we sharpen it to $$ \boldsymbolω(r) \approx \exp (-c| \ln r|^{\frac1N}); $$ for $p>\max\{2,N\}$, we derive an unexpected Hölder modulus. |
| title | Improved moduli of continuity for degenerate phase transitions |
| topic | Analysis of PDEs 35K65, 35K92, 35B65, 76S05, 80A22 |
| url | https://arxiv.org/abs/2408.11555 |