Regularity for a fractional p-Laplace equation

Abstract

In this note we consider regularity theory for a fractional $p$-Laplace operator which arises in the complex interpolation of the Sobolev spaces, the $H^{s,p}$-Laplacian. We obtain the natural analogue to the classical $p$-Laplacian situation, namely $C_{loc}^{s+\alpha }$-regularity for the homogeneous equation.