Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces. (March 2022)

• Record Type: Journal Article
• Authors: Bal, Kaushik; Mohanta, Kaushik; Roy, Prosenjit; Sk, Firoj
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: 35B27 -- 46E35 -- 49J52; Fractional Hardy inequality -- Regional fractional Poincaré inequality -- Fractional Poincaré inequality -- Fractional Orlicz Sobolev spaces -- Unbounded domains; 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.2021.112697
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We provide sufficient conditions for boundary Hardy inequality to hold in bounded Lipschitz domains, complement of a point (the so called point Hardy inequality), domain above the graph of a Lipschitz function, complement of a bounded Lipschitz domain in fractional Orlicz-Sobolev setting. As a consequence we get sufficient conditions for regional fractional Orlicz Poincaré inequality in bounded Lipschitz domains. Necessary conditions for fractional Orlicz Hardy and regional fractional Orlicz Poincaré inequalities are also given for bounded Lipschitz domains. Various sufficient conditions on open sets are provided for fractional Orlicz Poincaré inequality and regional fractional Orlicz Poincaré inequality to hold.