Regularity for the normalized p-Laplacian equation with an arbitrary degeneracy law
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918194005934080 |
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| author | Alcantara, Claudemir Santos, Makson |
| author_facet | Alcantara, Claudemir Santos, Makson |
| contents | We examine the interior regularity of solutions to a degenerate normalized $p$-Laplace equation, where the degeneracy is governed by a modulus of continuity whose inverse satisfies a Dini continuity condition. We prove that under very general assumptions on the degeneracy law, solutions belong to the $C^1$ class. We argue by approximating the solutions by a sequence of hyperplanes, which allows us to prove the desired regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity for the normalized p-Laplacian equation with an arbitrary degeneracy law Alcantara, Claudemir Santos, Makson Analysis of PDEs 35B65, 35J60, 35J70, 35D40 We examine the interior regularity of solutions to a degenerate normalized $p$-Laplace equation, where the degeneracy is governed by a modulus of continuity whose inverse satisfies a Dini continuity condition. We prove that under very general assumptions on the degeneracy law, solutions belong to the $C^1$ class. We argue by approximating the solutions by a sequence of hyperplanes, which allows us to prove the desired regularity. |
| title | Regularity for the normalized p-Laplacian equation with an arbitrary degeneracy law |
| topic | Analysis of PDEs 35B65, 35J60, 35J70, 35D40 |
| url | https://arxiv.org/abs/2511.07356 |