Fine boundary regularity for the degenerate fractional p-Laplacian

We consider a nonlocal equation driven by the fractional p-Laplacian (-Delta)(p)(s) with s is an element of]0,1[and p >= 2 (degenerate case), with a bounded reaction f and Dirichlet type conditions in a smooth domain Omega. 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(Omega)(s) is an element of C-alpha ((Omega) over bar) for some alpha is an element of]0,1[, d(Omega) being the distance from the boundary. (C) 2020 Elsevier Inc. All rights reserved.