Volume 19, Number 4, October-December 2013
|Page(s)||931 - 946|
|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
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.