Fine boundary regularity for the degenerate fractional p-Laplacian

Abstract

We consider a nonlocal equation driven by the fractional p-Laplacian (−Δ)ps 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 Hölder regularity up to the boundary, that is, u/dΩs∈Cα(Ω‾) for some α∈]0,1[, dΩ being the distance from the boundary.