Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913416155758592 |
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| author | Hernández-Santamaría, Víctor Ríos, Luis Fernando López Saldaña, Alberto |
| author_facet | Hernández-Santamaría, Víctor Ríos, Luis Fernando López Saldaña, Alberto |
| contents | We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the Kelvin transform and direct computations. As applications of our results, we show a Hopf-type Lemma for nonnegative weak solutions and the uniqueness of solutions to some nonlinear problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_18033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian Hernández-Santamaría, Víctor Ríos, Luis Fernando López Saldaña, Alberto Analysis of PDEs 35S15, 35B65, 35A02 We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the Kelvin transform and direct computations. As applications of our results, we show a Hopf-type Lemma for nonnegative weak solutions and the uniqueness of solutions to some nonlinear problems. |
| title | Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian |
| topic | Analysis of PDEs 35S15, 35B65, 35A02 |
| url | https://arxiv.org/abs/2401.18033 |