Maximum principles, Liouville theorem and symmetry results for the fractional g-Laplacian. (November 2021)

• Record Type: Journal Article
• Authors: Molina, Sandra; Salort, Ariel; Vivas, Hernán
• Is Part Of: Nonlinear analysis. Volume 212(2021)
• Publication Date: 2021-11
• Subjects: 35J62 -- 35B65; Fractional g-Laplacian -- Maximum principles -- Qualitative properties; 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.2021.112465
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study different maximum principles for non-local non-linear operators with non-standard growth that arise naturally in the context of fractional Orlicz–Sobolev spaces and whose most notable representative is the fractional g -Laplacian: ( − Δ g ) s u ( x ) ≔ p.v ∫ R n g u ( x ) − u ( y ) | x − y | s d y | x − y | n + s, being g the derivative of a Young function. We further derive qualitative properties of solutions such as a Liouville type theorem and symmetry results and present several possible extensions and some interesting open questions. These are the first results of this type proved in this setting.