Hopf’s lemma for parabolic equations involving a generalized tempered fractional p-Laplacian

Abstract

In this paper, we study a nonlinear system involving a generalized tempered fractional p-Laplacian in B 1(0):∂tu(x,t)+(−Δ−λf)psu(x,t)=g(t,u(x,t)),(x,t)∈B1(0)×[0,+∞),u(x)=0,(x,t)∈B1c(0)×[0,+∞), $$\begin{cases}_{t}u\left(x,t\right)+{\left(-{\Delta}-{\lambda }_{f}\right)}_{p}^{s}u\left(x,t\right)=g\left(t,u\left(x,t\right)\right),\quad \hfill & \left(x,t\right)\in {B}_{1}\left(0\right){\times}\left[0,+\infty \right),\hfill \\ u\left(x\right)=0,\quad \hfill & \left(x,t\right)\in {B}_{1}^{c}\left(0\right){\times}\left[0,+\infty \right),\hfill \end{cases}$$

Keywords

• hopf’s lemma
• a generalized tempered fractional p-laplacian
• parabolic fractional laplacian
• maximum principle
• primary 35r11
• secondary 35j92