Sobolev $(p,q)$-extension operators and Neumann eigenvalues
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910164151435264 |
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| author | Gol'dshtein, Vladimir Ukhlov, Alexander |
| author_facet | Gol'dshtein, Vladimir Ukhlov, Alexander |
| contents | In this article, we consider $(p,q)$-extension operators, $1 < q \le p < \infty$, on Sobolev spaces. Based on composition operators on Sobolev spaces, we construct the extension operators in outward cuspidal domains with estimates of their norms. Using these $(p,q)$-extension operators, we prove estimates for the non-linear Neumann eigenvalues of the $p$-Laplace operator in outward cuspidal domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sobolev $(p,q)$-extension operators and Neumann eigenvalues Gol'dshtein, Vladimir Ukhlov, Alexander Analysis of PDEs 46E35, 30C65, 35P15 In this article, we consider $(p,q)$-extension operators, $1 < q \le p < \infty$, on Sobolev spaces. Based on composition operators on Sobolev spaces, we construct the extension operators in outward cuspidal domains with estimates of their norms. Using these $(p,q)$-extension operators, we prove estimates for the non-linear Neumann eigenvalues of the $p$-Laplace operator in outward cuspidal domains. |
| title | Sobolev $(p,q)$-extension operators and Neumann eigenvalues |
| topic | Analysis of PDEs 46E35, 30C65, 35P15 |
| url | https://arxiv.org/abs/2411.15932 |