Higher Holder regularity for the fractional p-Laplacian in the superquadratic case

We prove higher Holder regularity for solutions of equations involving the fractional p-Laplacian of order s, when p >= 2 and 0 < s < 1. In particular, we provide an explicit Holder exponent for solutions of the non-homogeneous equation with data in L-q and q > N/(sp), which is almost sharp whenever sp <= (p 1) + N/q. The result is new already for the homogeneous equation. (C) 2018 Elsevier Inc. All rights reserved.