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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/2411.00449 |
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| _version_ | 1866917825610776576 |
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| author | Fan, Linlin Cao, Linfen Zhao, Peibiao |
| author_facet | Fan, Linlin Cao, Linfen Zhao, Peibiao |
| contents | In this paper, we study a nonlinear system involving a generalized tempered fractional $p$-Laplacian in $B_{1}(0)$: \begin{equation*} \left\{ \begin{array}{ll} \partial_tu(x,t)+(-Δ-λ_{f})_{p}^{s}u(x,t)=g(t,u(x,t)), &(x,t)\in B_{1}(0)\times[0,+\infty),\\ u(x)=0,&(x,t)\in B_{1}^{c}(0)\times[0,+\infty), \end{array} \right. \end{equation*} where $0<s<1$, $p>2,\ n\geq2$. We establish Hopf's lemma for parabolic equations involving a generalized tempered fractional $p$-Laplacian. Hopf's lemma will become powerful tools in obtaining qualitative properties of solutions for nonlocal parabolic equations.. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hopf's lemma for parabolic equations involving a generalized tempered fractional $p$-Laplacian Fan, Linlin Cao, Linfen Zhao, Peibiao Analysis of PDEs In this paper, we study a nonlinear system involving a generalized tempered fractional $p$-Laplacian in $B_{1}(0)$: \begin{equation*} \left\{ \begin{array}{ll} \partial_tu(x,t)+(-Δ-λ_{f})_{p}^{s}u(x,t)=g(t,u(x,t)), &(x,t)\in B_{1}(0)\times[0,+\infty),\\ u(x)=0,&(x,t)\in B_{1}^{c}(0)\times[0,+\infty), \end{array} \right. \end{equation*} where $0<s<1$, $p>2,\ n\geq2$. We establish Hopf's lemma for parabolic equations involving a generalized tempered fractional $p$-Laplacian. Hopf's lemma will become powerful tools in obtaining qualitative properties of solutions for nonlocal parabolic equations.. |
| title | Hopf's lemma for parabolic equations involving a generalized tempered fractional $p$-Laplacian |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.00449 |