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Homogenization in Sobolev Spaces with Nonstandard Growth : Brief Review of Methods and Applications
Joint Authors
Pankratov, Leonid
Amaziane, Brahim
Source
International Journal of Differential Equations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-15
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
We review recent results on the homogenization in Sobolev spaces with variable exponents.
In particular, we are dealing with the Γ-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.
American Psychological Association (APA)
Amaziane, Brahim& Pankratov, Leonid. 2013. Homogenization in Sobolev Spaces with Nonstandard Growth : Brief Review of Methods and Applications. International Journal of Differential Equations،Vol. 2013, no. 2013, pp.1-16.
https://search.emarefa.net/detail/BIM-491103
Modern Language Association (MLA)
Amaziane, Brahim& Pankratov, Leonid. Homogenization in Sobolev Spaces with Nonstandard Growth : Brief Review of Methods and Applications. International Journal of Differential Equations No. 2013 (2013), pp.1-16.
https://search.emarefa.net/detail/BIM-491103
American Medical Association (AMA)
Amaziane, Brahim& Pankratov, Leonid. Homogenization in Sobolev Spaces with Nonstandard Growth : Brief Review of Methods and Applications. International Journal of Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-16.
https://search.emarefa.net/detail/BIM-491103
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-491103