Interior and up to the boundary regularity for the fractional $g$-Laplacian: the convex case

Julián Fernández Bonder, Ariel Salort, Hernán Vivas

Published 2020-08-12Version 1

We establish interior and up to the boundary H\"older regularity estimates for weak solutions of the Dirichlet problem for the fractional $g-$Laplacian with bounded right hand side and $g$ convex. These are the first regularity results available in the literature for integro-differential equations in the context of fractional Orlicz-Sobolev spaces.