Isocapacitary constants for the $p$-Laplacian on compact manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918266737262592 |
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| author | Wang, Lili Wang, Tao |
| author_facet | Wang, Lili Wang, Tao |
| contents | In this paper, we introduce Steklov and Neumann isocapacitary constants for the $p$-Laplacian on compact manifolds. These constants yield two-sided bounds for the $(p,α)$-Sobolev constants, which degenerate to upper and lower bounds for the first nontrivial Steklov and Neumann eigenvalues of the $p$-Laplacian when $α= 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isocapacitary constants for the $p$-Laplacian on compact manifolds Wang, Lili Wang, Tao Differential Geometry Analysis of PDEs 35P15, 35P30, 58J50 In this paper, we introduce Steklov and Neumann isocapacitary constants for the $p$-Laplacian on compact manifolds. These constants yield two-sided bounds for the $(p,α)$-Sobolev constants, which degenerate to upper and lower bounds for the first nontrivial Steklov and Neumann eigenvalues of the $p$-Laplacian when $α= 1$. |
| title | Isocapacitary constants for the $p$-Laplacian on compact manifolds |
| topic | Differential Geometry Analysis of PDEs 35P15, 35P30, 58J50 |
| url | https://arxiv.org/abs/2512.24725 |