Global Hölder regularity for eigenfunctions of the fractional $g$-Laplacian

Abstract

We establish global Hölder regularity for eigenfunctions of the fractional $g-$Laplacian with Dirichlet boundary conditions where $g=G^{\prime }$ and $G$ is a Young functions satisfying the so called ${\Delta }_2$ condition. Our results apply to more general semilinear equations of the form $(-{\Delta }_g{)}^{s}u=f(u)$.