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

FERNÁNDEZ BONDER, JULIÁN; SALORT, ARIEL; VIVAS, HERNÁN

JOURNAL OF NONLINEAR ANALYSIS

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2022 vol. 223

0362-546X

We establish interior and up to the boundary Hölder 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.