Some remarks on two-scale convergence and periodic unfolding.
type: Item
instance of: scholarly article
title: Some remarks on two-scale convergence and periodic unfolding.
zbMATH Open document ID: 1265.35017
author: Nils Svanstedt
author: Jan Franců
published in: Applications of Mathematics
publication date: 2012-10-29T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/142904
review text: The author introduces the adjoint definition of the two-scale convergence, based on the periodic unfolding, in comparison with the classical one. Such approach avoids most problems of the admissibility (specific type of regularity) of test functions. The principal part of the paper gives a self-contained introduction to the two-scale convergence. It includes proofs relating to its classical definition and dual definitions, to the periodic unfolding extended by zero, as well as on that (original one) extended by identity, and to its properties in standard Lebesgue spaces \(L^p\) (\(p>1\)) and properties of gradients from corresponding Sobolev spaces \(W^{1,p}\). The last section presents some ideas for generalization of such results to the non-periodic homogenization, referring to the two-scale transform, the integral conservation and the general \(\Sigma \)-convergence by \textit{G. Nguetseng} and \textit{N. Svanstedt} [Banach J. Math. Anal. 5, No. 1, 101--135 (2011; Zbl 1229.46035)].
Mathematics Subject Classification ID: 35B27
zbMATH DE Number: 6099665
zbMATH Keywords: two-scale convergence
zbMATH Keywords: unfolding
zbMATH Keywords: homogenization
reviewed by: Josef Vala
MaRDI profile type: Publication
OpenAlex ID: W2064716340
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DOI: 10.1007/S10492-012-0021-Z
description: scientific article; zbMATH DE number 6099665