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Main Authors: Fan, Linlin, Cao, Linfen, Zhao, Peibiao
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2411.00449
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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..
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publishDate 2024
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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