Lipschitz regularity for fractional $p$-Laplacian with coercive gradients
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915924274053120 |
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| author | Biswas, Anup Sen, Aniket Topp, Erwin |
| author_facet | Biswas, Anup Sen, Aniket Topp, Erwin |
| contents | In this article, we study nonlinear nonlocal equations with coercive gradient nonlinearity of the form \[ (-Δ_p)^s u(x) + H(x, \nabla u) = f, \] where $f$ is Lipschitz continuous. We show that any viscosity solution $u$ is locally Lipschitz continuous, provided \[ p \in \left(1, \frac{2}{1-s}\right) \cup (1, m+1). \] We also establish Hölder continuity of subsolutions. Furthermore, in the case $f=0$ and $H$ is independent of $x$, we prove that the equation admits only the trivial solution in the class of bounded solutions, for all $m, p \in (1,\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07489 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lipschitz regularity for fractional $p$-Laplacian with coercive gradients Biswas, Anup Sen, Aniket Topp, Erwin Analysis of PDEs In this article, we study nonlinear nonlocal equations with coercive gradient nonlinearity of the form \[ (-Δ_p)^s u(x) + H(x, \nabla u) = f, \] where $f$ is Lipschitz continuous. We show that any viscosity solution $u$ is locally Lipschitz continuous, provided \[ p \in \left(1, \frac{2}{1-s}\right) \cup (1, m+1). \] We also establish Hölder continuity of subsolutions. Furthermore, in the case $f=0$ and $H$ is independent of $x$, we prove that the equation admits only the trivial solution in the class of bounded solutions, for all $m, p \in (1,\infty)$. |
| title | Lipschitz regularity for fractional $p$-Laplacian with coercive gradients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.07489 |