| Issue |
ESAIM: COCV
Volume 19, Number 4, October-December 2013
|
|
|---|---|---|
| Page(s) | 931 - 946 | |
| DOI | https://doi.org/10.1051/cocv/2012039 | |
| Published online | 04 July 2013 | |
Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit
1 University Bordeaux, IMB, UMR 5251, 33400 Talence, France
Kevin.Santugini@math.u-bordeaux1.fr
2 CNRS, IMB, UMR 5251, 33400 Talence, France
3 INRIA, 33400 Talence, France
Received: 15 September 2011
Revised: 7 June 2012
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.
Mathematics Subject Classification: 35B27
Key words: Homogenization / two-scale convergence
© EDP Sciences, SMAI, 2013
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