Liouville results for supersolutions of fractional $p$-Laplacian equations with gradient nonlinearities
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918321839931392 |
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| author | Bhakta, Mousomi Biswas, Anup Sen, Aniket |
| author_facet | Bhakta, Mousomi Biswas, Anup Sen, Aniket |
| contents | We prove that any nonnegative viscosity solution of the inequality $$(-Δ_p)^s u(x) \geq u^{t} |\nabla u|^{m}\quad \text{ in }\; \mathbb{R}^N,\; N\geq 2,$$ must be constant. This result holds for parameters $p\in (1, \infty), s\in (0, 1)$, $t, m\geq 0$, satisfying $$t (N-sp) + m(N-(sp-p+1)) < N(p-1),$$ with the additional condition that either $m\leq p-1$ if $p-1<sp$, or $m<sp$ if $p-1\geq sp$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06334 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Liouville results for supersolutions of fractional $p$-Laplacian equations with gradient nonlinearities Bhakta, Mousomi Biswas, Anup Sen, Aniket Analysis of PDEs 35B53, 35J60, 35J92, 35J70 We prove that any nonnegative viscosity solution of the inequality $$(-Δ_p)^s u(x) \geq u^{t} |\nabla u|^{m}\quad \text{ in }\; \mathbb{R}^N,\; N\geq 2,$$ must be constant. This result holds for parameters $p\in (1, \infty), s\in (0, 1)$, $t, m\geq 0$, satisfying $$t (N-sp) + m(N-(sp-p+1)) < N(p-1),$$ with the additional condition that either $m\leq p-1$ if $p-1<sp$, or $m<sp$ if $p-1\geq sp$. |
| title | Liouville results for supersolutions of fractional $p$-Laplacian equations with gradient nonlinearities |
| topic | Analysis of PDEs 35B53, 35J60, 35J92, 35J70 |
| url | https://arxiv.org/abs/2511.06334 |