Calculus of Variations and Geometric Measure Theory

L. Brasco - E. Lindgren

Higher Sobolev regularity for the fractional $p-$Laplace equation in the superquadratic case

created by brasco on 02 Aug 2015
modified on 30 Mar 2016


Accepted Paper

Inserted: 2 aug 2015
Last Updated: 30 mar 2016

Journal: Adv. Math.
Pages: 36
Year: 2015


We prove that for $p\ge 2$ solutions of equations modeled by the fractional $p-$Laplacian improve their regularity on the scale of fractional Sobolev spaces. Moreover, under certain precise conditions, they are in $W^{1,p}_{loc}$ and their gradients are in a fractional Sobolev space as well. The relevant estimates are stable as the fractional order of differentiation $s$ reaches $1$.

Keywords: Fractional $p-$Laplacian, nonlocal elliptic equations, Besov regularity