A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces

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 inclu...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 175; pp. 1 - 27
Main Author: Chlebicka, Iwona
Format: Journal Article
Language:English
Published: Elmsford Elsevier Ltd 01.10.2018
Elsevier BV
Subjects:
Anisotropy
Differential equations
Elliptic problems
Existence of solutions
Inhomogeneity
Lavrentiev’s phenomenon
Mathematical functions
Musielak–Orlicz spaces
Nonlinear equations
Parabolic problems
Partial differential equations
Renormalized solutions
35J60
46E30
35D30
Elliptic problems
Parabolic problems
Musielak–Orlicz spaces
Renormalized solutions
Existence of solutions
Lavrentiev’s phenomenon
ISSN:0362-546X, 1873-5215
Online Access:Get full text
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Summary: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.
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2018.05.003