Fine boundary regularity for the degenerate fractional p-Laplacian

Abstract We consider a nonlocal equation driven by the fractional p-Laplacian ( − Δ ) p s with s ∈ ] 0 , 1 [ and p ⩾ 2 (degenerate case), with a bounded reaction f and Dirichlet type conditions in a smooth domain Ω. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution u of such equation exhibits a weighted Holder regularity up to the boundary, that is, u / d Ω s ∈ C α ( Ω ‾ ) for some α ∈ ] 0 , 1 [ , d Ω being the distance from the boundary.