Regularity for a fractional p-Laplace equation

TL;DR

This paper establishes local regularity results for solutions to a fractional p-Laplace equation, extending classical regularity theory to the fractional setting within Sobolev space interpolation.

Contribution

It provides the first regularity result for the fractional p-Laplace operator, showing local Hölder continuity akin to the classical p-Laplacian case.

Findings

Proves local Hölder regularity for solutions

Extends classical p-Laplacian regularity to fractional case

Connects fractional p-Laplacian to Sobolev space interpolation

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 $C^{s+\alpha}_{loc}$-regularity for the homogeneous equation.