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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Podrobná bibliografia
Vydané v:Nonlinear analysis Ročník 175; s. 1 - 27
Hlavný autor: Chlebicka, Iwona
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elmsford Elsevier Ltd 01.10.2018
Elsevier BV
Predmet:
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
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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.
AbstractList 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.
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.
Author Chlebicka, Iwona
Author_xml – sequence: 1
  givenname: Iwona
  orcidid: 0000-0003-2053-5988
  surname: Chlebicka
  fullname: Chlebicka, Iwona
  email: iskrzypczak@mimuw.edu.pl
  organization: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland
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Keywords 35J60
46E30
35D30
Elliptic problems
Parabolic problems
Musielak–Orlicz spaces
Renormalized solutions
Existence of solutions
Lavrentiev’s phenomenon
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Snippet The Musielak–Orlicz setting unifies variable exponent, Orlicz, weighted Sobolev, and double-phase spaces. They inherit technical difficulties resulting from...
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SubjectTerms 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
Title A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces
URI https://dx.doi.org/10.1016/j.na.2018.05.003
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Volume 175
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