Calculus of Variations and Geometric Measure Theory

L. Brasco - E. Lindgren - A. Schikorra

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

created by brasco on 17 Nov 2017
modified on 29 Aug 2018


Accepted Paper

Inserted: 17 nov 2017
Last Updated: 29 aug 2018

Journal: Adv. Math.
Pages: 44
Year: 2018


We prove higher H\"older 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 H\"older exponent for solutions of the non-homogeneous equation with data in $L^q$ and $q>N/(s\,p)$, which is almost sharp whenever $s\,p\leq (p-1)+N/q$. The result is new already for the homogeneous equation.

Keywords: Fractional p-Laplacian, nonlocal elliptic equations, H\"older regularity