A note on global regularity for the weak solutions of fractional p-Laplacian equations

TL;DR

This paper establishes boundary regularity for weak solutions of fractional p-Laplacian equations with bounded reactions, using barrier methods to prove H"older continuity up to the boundary for both singular and degenerate cases.

Contribution

It provides the first boundary regularity results for fractional p-Laplacian equations with bounded reactions, covering both singular and degenerate regimes.

Findings

Weak solutions are H"older continuous up to the boundary.

Boundary regularity holds for both 1<p<2 and p>2 cases.

Barrier arguments effectively establish regularity results.

Abstract

We consider a boundary value problem driven by the fractional p-Laplacian operator with a bounded reaction term. By means of barrier arguments, we prove H\"older regularity up to the boundary for the weak solutions, both in the singular (1<p<2) and the degenerate (p>2) case.