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