A Talenti-type comparison theorem for the $p$-Laplacian on $\mathrm{RCD}(K,N)$ spaces and some applications
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909078604742656 |
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| author | Wu, Wenjing |
| author_facet | Wu, Wenjing |
| contents | In this paper, we prove a Talenti-type comparison theorem for the $p$-Laplacian with Dirichlet boundary conditions on open subsets of a $\mathrm{RCD}(K,N)$ space with $K>0$ and $N\in (1,\infty)$. The obtained Talenti-type comparison theorem is sharp, rigid and stable with respect to measured Gromov-Hausdorff topology. As an application of such Talenti-type comparison, we establish a sharp and rigid reverse Hölder inequality for first eigenfunctions of the $p$-Laplacian and a related quantitative stability result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Talenti-type comparison theorem for the $p$-Laplacian on $\mathrm{RCD}(K,N)$ spaces and some applications Wu, Wenjing Differential Geometry Metric Geometry In this paper, we prove a Talenti-type comparison theorem for the $p$-Laplacian with Dirichlet boundary conditions on open subsets of a $\mathrm{RCD}(K,N)$ space with $K>0$ and $N\in (1,\infty)$. The obtained Talenti-type comparison theorem is sharp, rigid and stable with respect to measured Gromov-Hausdorff topology. As an application of such Talenti-type comparison, we establish a sharp and rigid reverse Hölder inequality for first eigenfunctions of the $p$-Laplacian and a related quantitative stability result. |
| title | A Talenti-type comparison theorem for the $p$-Laplacian on $\mathrm{RCD}(K,N)$ spaces and some applications |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2401.11456 |