Hopf's lemmas and boundary behaviour of solutions to the fractional Laplacian in Orlicz-Sobolev spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917842568347648 |
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| author | Ochoa, Pablo Salort, Ariel |
| author_facet | Ochoa, Pablo Salort, Ariel |
| contents | In this article we study different extensions of the celebrated Hopf's boundary lemma within the context of a family of nonlocal, nonlinear and nonstandard growth operators. More precisely, we examine the behavior of solutions of the fractional $a-$Laplacian operator near the boundary of a domain satisfying the interior ball condition. Our approach addresses problems involving both constant-sign and sign-changing potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hopf's lemmas and boundary behaviour of solutions to the fractional Laplacian in Orlicz-Sobolev spaces Ochoa, Pablo Salort, Ariel Analysis of PDEs In this article we study different extensions of the celebrated Hopf's boundary lemma within the context of a family of nonlocal, nonlinear and nonstandard growth operators. More precisely, we examine the behavior of solutions of the fractional $a-$Laplacian operator near the boundary of a domain satisfying the interior ball condition. Our approach addresses problems involving both constant-sign and sign-changing potentials. |
| title | Hopf's lemmas and boundary behaviour of solutions to the fractional Laplacian in Orlicz-Sobolev spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.13498 |