A Hopf lemma for the regional fractional Laplacian

2021/12/17 by Abatangelo, Nicola, Fall, Mouhamed Moustapha, Temgoua, Remi Yvant
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.09522

Abstract

We provide a Hopf boundary lemma for the regional fractional Laplacian (-Δ)^s_Ω, with Ω⊂ℝ^N a bounded open set. More precisely, given u a pointwise or weak super-solution of the equation (-Δ)^s_Ω u = c(x)u in Ω, we show that the ratio u(x)/(dist(x,∂Ω))^2s-1 is strictly positive as x approaches the boundary ∂Ω of Ω. We also prove a strong maximum principle for distributional super-solutions.

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