Fine boundary continuity for degenerate double-phase diffusion
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913260786155520 |
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| author | Ciani, Simone Henriques, Eurica Skrypnik, Igor |
| author_facet | Ciani, Simone Henriques, Eurica Skrypnik, Igor |
| contents | We study the boundary behavior of solutions to parabolic double-phase equations through the celebrated Wiener's sufficiency criterion. The analysis is conducted for cylindrical domains and the regularity up to the lateral boundary is shown in terms of either its $p$ or $q$ capacity, depending on whether the phase vanishes at the boundary or not. Eventually we obtain a fine boundary estimate that, when considering uniform geometric conditions as density or fatness, leads us to the boundary Hölder continuity of solutions. In particular, the double-phase elicits new questions on the definition of an adapted capacity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fine boundary continuity for degenerate double-phase diffusion Ciani, Simone Henriques, Eurica Skrypnik, Igor Analysis of PDEs 35B65, 35B45, 35K65 We study the boundary behavior of solutions to parabolic double-phase equations through the celebrated Wiener's sufficiency criterion. The analysis is conducted for cylindrical domains and the regularity up to the lateral boundary is shown in terms of either its $p$ or $q$ capacity, depending on whether the phase vanishes at the boundary or not. Eventually we obtain a fine boundary estimate that, when considering uniform geometric conditions as density or fatness, leads us to the boundary Hölder continuity of solutions. In particular, the double-phase elicits new questions on the definition of an adapted capacity. |
| title | Fine boundary continuity for degenerate double-phase diffusion |
| topic | Analysis of PDEs 35B65, 35B45, 35K65 |
| url | https://arxiv.org/abs/2403.06550 |