Global Hölder regularity for the fractional $p$-Laplacian

Abstract

By virtue of barrier arguments we prove C^\alpha -regularity up to the boundary for the weak solutions of a non-local, non-linear problem driven by the fractional p -Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular ( p < 2 ) of degenerate ( p > 2 ) case.