Homogenization in Sobolev spaces with nonstandard growth: brief review of methods and applications
type: Item
instance of: scholarly article
title: Homogenization in Sobolev spaces with nonstandard growth: brief review of methods and applications
zbMATH Open document ID: 1270.35054
DOI: 10.1155/2013/693529
author: Brahim Amaziane
author: Leonid Pankratov
published in: International Journal of Differential Equations
publication date: 2013-06-10T00:00:00Z
review text: Summary: We review recent results on the homogenization in Sobolev spaces with variable exponents. In particular, we are dealing with the \(\Gamma\)-convergence of variational functionals with rapidly oscillating coefficients, the homogenization of the Dirichlet and Neumann variational problems in strongly perforated domains, as well as double porosity type problems. The growth functions also depend on the small parameter characterizing the scale of the microstructure. The homogenization results are obtained by the method of local energy characteristics. We also consider a parabolic double porosity type problem, which is studied by combining the variational homogenization approach and the two-scale convergence method. Results are illustrated with periodic examples, and the problem of stability in homogenization is discussed.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35-02
zbMATH DE Number: 6172135
zbMATH Keywords: Sobolev spaces with variable exponents
zbMATH Keywords: local energy characteristics
zbMATH Keywords: double porosity type problem
zbMATH Keywords: two-scale convergence
Wikidata QID: Q58923622
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/693529
OpenAlex ID: W2076894317
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description: scientific article; zbMATH DE number 6172135