A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces. (October 2018)

• Record Type: Journal Article
• Authors: Chlebicka, Iwona
• Is Part Of: Nonlinear analysis. Volume 175(2018)
• Page Start: 1
• Page End: 27
• Publication Date: 2018-10
• Subjects: 46E30 -- 35J60 -- 35D30; Elliptic problems -- Parabolic problems -- Existence of solutions -- Musielak–Orlicz spaces -- Renormalized solutions -- Lavrentiev's phenomenon; 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.2018.05.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The Musielak–Orlicz setting unifies variable exponent, Orlicz, weighted Sobolev, and double-phase spaces. They inherit technical difficulties resulting from general growth and inhomogeneity. In this survey we present an overview of developments of the theory of existence of PDEs in the setting including reflexive and non-reflexive cases, as well as isotropic and anisotropic ones. Particular attention is paid to problems with data below natural duality in absence of Lavrentiev's phenomenon.