Lipschitz regularity for parabolic fractional $p$-Laplace equations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917358079049728 |
|---|---|
| author | Prasad, Harsh |
| author_facet | Prasad, Harsh |
| contents | We prove that local weak solutions to nonlocal parabolic $p$-Laplace equations are locally Lipschitz continuous in space, uniformly in time for every $1<p<\infty$ and $s \in (0,1)$ whenever $sp > p-1$. Our results hold for symmetric, translation-invariant kernels satisfying standard ellipticity bounds, including kernels that may be discontinuous and require only that the tail of the solution be bounded. In the linear case, our proof provides a different route avoiding blow up arguments and Liouville theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lipschitz regularity for parabolic fractional $p$-Laplace equations Prasad, Harsh Analysis of PDEs 35B65, 35K92, 35R09, 35D30 We prove that local weak solutions to nonlocal parabolic $p$-Laplace equations are locally Lipschitz continuous in space, uniformly in time for every $1<p<\infty$ and $s \in (0,1)$ whenever $sp > p-1$. Our results hold for symmetric, translation-invariant kernels satisfying standard ellipticity bounds, including kernels that may be discontinuous and require only that the tail of the solution be bounded. In the linear case, our proof provides a different route avoiding blow up arguments and Liouville theorems. |
| title | Lipschitz regularity for parabolic fractional $p$-Laplace equations |
| topic | Analysis of PDEs 35B65, 35K92, 35R09, 35D30 |
| url | https://arxiv.org/abs/2603.21956 |