Global H\"older regularity for eigenfunctions of the fractional $g$-Laplacian

TL;DR

This paper proves that eigenfunctions of the fractional g-Laplacian operator are globally H"older continuous under certain conditions, extending regularity results to more general semilinear equations.

Contribution

It establishes global H"older regularity for eigenfunctions of the fractional g-Laplacian with Dirichlet boundary conditions, generalizing previous results to broader classes of equations.

Findings

Eigenfunctions are globally H"older continuous.

Results apply to semilinear equations with fractional g-Laplacian.

Extends regularity theory to more general operators.

Abstract

We establish global H\"older regularity for eigenfunctions of the fractional $g-$Laplacian with Dirichlet boundary conditions where $g=G'$ and $G$ is a Young functions satisfying the so called $\Delta_2$ condition. Our results apply to more general semilinear equations of the form $(-\Delta_g)^s u = f(u)$.