Abstract
We provide a Hopf boundary lemma for the regional fractional Laplacian (-Delta )^s_{Omega }, with Omega subset mathbb {R}^N a bounded open set. More precisely, given u a pointwise or weak super-solution of the equation (-Delta )^s_{Omega }u=c(x)u in Omega, we show that the ratio u(x)/(text {dist}(x,partial Omega ))^{2s-1} is strictly positive as x approaches the boundary partial Omega of Omega. We also prove a strong maximum principle for distributional super-solutions.
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