Parabolic weighted Sobolev–Poincaré type inequalities. (May 2022)

• Record Type: Journal Article
• Authors: Diening, Lars; Lee, Mikyoung; Ok, Jihoon
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: 46E35 -- 35K10 -- 35A23; Sobolev–Poincaré inequality -- Parabolic equation -- Weight -- Parabolic Muckenhoupt class; 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.2021.112772
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We derive weighted Sobolev–Poincaré type inequalities in function spaces concerned with parabolic partial differential equations. We consider general weights depending on both space and time variables belonging to a Muckenhoupt class, so-called the parabolic A p -class, where only the parabolic cubes are involved in the definition.