H\"older regularity for fractional $p$-Laplace equations

TL;DR

This paper presents a new proof technique for establishing H"older regularity of solutions to fractional p-Laplacian equations, replacing discrete iteration with a continuous approach, thus advancing the understanding of nonlocal elliptic equations.

Contribution

It introduces an alternative continuous iteration method for proving regularity, offering a novel perspective compared to traditional discrete De Giorgi techniques.

Findings

Proves H"older regularity for fractional p-Laplacian solutions

Develops a continuous iteration approach for nonlocal equations

Provides insights aligned with Granucci's ideas

Abstract

We give an alternative proof for H\"older regularity for weak solutions of nonlocal elliptic quasilinear equations modelled on the fractional p-Laplacian where we replace the discrete De Giorgi iteration on a sequence of concentric balls by a continuous iteration. This work can be viewed as the nonlocal counterpart to the ideas developed by Tiziano Granucci.