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Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit

Published online by Cambridge University Press:  04 July 2013

Kévin Santugini
Kévin Santugini*
Affiliation:
University Bordeaux, IMB, UMR 5251, 33400 Talence, France. [email protected] CNRS, IMB, UMR 5251, 33400 Talence, France INRIA, 33400 Talence, France
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Abstract

In this paper, we consider two-scale limits obtained with increasing homogenization periods, each period being an entire multiple of the previous one. We establish that, up to a measure preserving rearrangement, these two-scale limits form a martingale which is bounded: the rearranged two-scale limits themselves converge both strongly in L2 and almost everywhere when the period tends to  +∞. This limit, called the Two-Scale Shuffle limit, contains all the information present in all the two-scale limits in the sequence.

Keywords

Homogenizationtwo-scale convergence
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 4 , October 2013 , pp. 931 - 946
Copyright
© EDP Sciences, SMAI, 2013

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