Hölder continuity up to the boundary for a class of fractional obstacle problems

Abstract

We deal with the obstacle problem for a class of nonlinear integro-differential operators, whose model is the fractional $p$-Laplacian with measurable coeffcients. In accordance with well-known results for the analog for the pure fractional Laplacian operator, the corresponding solutions inherit regularity properties from the obstacle, both in the case of boundedness, continuity, and Hölder continuity, up to the boundary.