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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/2401.09982 |
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| _version_ | 1866916750200668160 |
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| author | Benatti, Luca Violo, Ivan Yuri |
| author_facet | Benatti, Luca Violo, Ivan Yuri |
| contents | We establish quantitative second-order Sobolev regularity for functions having a $2$-integrable $p$-Laplacian in bounded RCD spaces, with $p$ in a suitable range. In the finite-dimensional case, we also obtain Lipschitz regularity under the assumption that $p$-Laplacian is sufficiently integrable. Our results cover both $p$-Laplacian eigenfunctions and $p$-harmonic functions having relatively compact level sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Second-order estimates for the $p$-Laplacian in RCD spaces Benatti, Luca Violo, Ivan Yuri Metric Geometry Analysis of PDEs Differential Geometry 35B65, 46E36, 30L15, 58J37, 47H14 We establish quantitative second-order Sobolev regularity for functions having a $2$-integrable $p$-Laplacian in bounded RCD spaces, with $p$ in a suitable range. In the finite-dimensional case, we also obtain Lipschitz regularity under the assumption that $p$-Laplacian is sufficiently integrable. Our results cover both $p$-Laplacian eigenfunctions and $p$-harmonic functions having relatively compact level sets. |
| title | Second-order estimates for the $p$-Laplacian in RCD spaces |
| topic | Metric Geometry Analysis of PDEs Differential Geometry 35B65, 46E36, 30L15, 58J37, 47H14 |
| url | https://arxiv.org/abs/2401.09982 |