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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.14534 |
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| _version_ | 1866912567660642304 |
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| author | Karrouchi, Yassin El Weth, Tobias |
| author_facet | Karrouchi, Yassin El Weth, Tobias |
| contents | Inspired by recent work of Ferone and Volzone arXiv:2007.13195, we derive sufficient conditions for the validity and non-validity of a boundary version of Talenti's comparison principle in the context of Dirichlet-Poisson problems for the fractional Laplacian $(-Δ)^s$ in the unit ball $Ω= B_1(0) \subset \mathbb{R}^N$. In particular, our results imply a universial failure of the classical pointwise Talenti inequality in the fractional radial context which sheds new light on the one-dimensional counterexamples given in arXiv:2007.13195. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a fractional boundary version of Talenti's inequality in the unit ball Karrouchi, Yassin El Weth, Tobias Analysis of PDEs Inspired by recent work of Ferone and Volzone arXiv:2007.13195, we derive sufficient conditions for the validity and non-validity of a boundary version of Talenti's comparison principle in the context of Dirichlet-Poisson problems for the fractional Laplacian $(-Δ)^s$ in the unit ball $Ω= B_1(0) \subset \mathbb{R}^N$. In particular, our results imply a universial failure of the classical pointwise Talenti inequality in the fractional radial context which sheds new light on the one-dimensional counterexamples given in arXiv:2007.13195. |
| title | On a fractional boundary version of Talenti's inequality in the unit ball |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.14534 |