Interior and up to the boundary regularity for the fractional g-Laplacian: The convex case. (October 2022)

• Record Type: Journal Article
• Authors: Fernández Bonder, Julián; Salort, Ariel; Vivas, Hernán
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: 35J62 -- 35B65; Fractional g−Laplacian -- Elliptic regularity -- Boundary regularity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113060
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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.