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Mathematics > Analysis of PDEs

arXiv:1804.04193 (math)
[Submitted on 11 Apr 2018 (v1), last revised 4 May 2018 (this version, v2)]

Title:A pocket guide to nonlinear differential equations in the Musielak--Orlicz spaces

Authors:Iwona Chlebicka
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Abstract:The Musielak--Orlicz setting unifies the 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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.04193 [math.AP]
  (or arXiv:1804.04193v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.04193
Journal reference: Nonlinear Analysis, 175 (2018), 1-27
Related DOI: https://doi.org/10.1016/j.na.2018.05.003

Submission history

From: Iwona Chlebicka [view email]
[v1] Wed, 11 Apr 2018 20:02:59 UTC (32 KB)
[v2] Fri, 4 May 2018 22:46:14 UTC (36 KB)
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