Higher Hölder regularity for the fractional $p-$Laplacian in the superquadratic case

Abstract

We prove higher Hölder regularity for solutions of equations involving the fractional $p-$Laplacian of order $s$, when $p\ge 2$ and $0<s<1$. In particular, we provide an explicit Hölder exponent for solutions of the non-homogeneous equation with data in $L^q$ and $q>N/(sp)$, which is almost sharp whenever $sp\le (p-1)+N/q$. The result is new already for the homogeneous equation.

arXiv comment44 pages. Corrected some minor misprints, added some references