Local and global $C^{1,β}$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914264813404160 |
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| author | Antonini, Carlo Alberto |
| author_facet | Antonini, Carlo Alberto |
| contents | We establish gradient Hölder continuity for solutions to quasilinear, uniformly elliptic equations, including $p$-Laplace and Orlicz-Laplace type operators. We revisit and improve upon the results existing in the literature, proving gradient regularity both in the interior and up to the boundary, under Dirichlet or Neumann boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local and global $C^{1,β}$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type Antonini, Carlo Alberto Analysis of PDEs 35D30, 35J60, 35J62, 35J66, 35J92, 49N60 We establish gradient Hölder continuity for solutions to quasilinear, uniformly elliptic equations, including $p$-Laplace and Orlicz-Laplace type operators. We revisit and improve upon the results existing in the literature, proving gradient regularity both in the interior and up to the boundary, under Dirichlet or Neumann boundary conditions. |
| title | Local and global $C^{1,β}$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type |
| topic | Analysis of PDEs 35D30, 35J60, 35J62, 35J66, 35J92, 49N60 |
| url | https://arxiv.org/abs/2601.07140 |