Homogenization at different linear scales, bounded martingales and the Two-Scale Shuffle limit
SANTUGINI-REPIQUET, Kévin
Institut de Mathématiques de Bordeaux [IMB]
Modélisation, contrôle et calcul [MC2]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation, contrôle et calcul [MC2]
SANTUGINI-REPIQUET, Kévin
Institut de Mathématiques de Bordeaux [IMB]
Modélisation, contrôle et calcul [MC2]
< Réduire
Institut de Mathématiques de Bordeaux [IMB]
Modélisation, contrôle et calcul [MC2]
Langue
en
Article de revue
Ce document a été publié dans
ESAIM: Control, Optimisation and Calculus of Variations. 2013-10-10, vol. 19, p. 931--946
EDP Sciences
Résumé en anglais
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 ...Lire la suite >
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 $\mathrm{L}^2$ and almost everywhere when the period tends to $+\infty$. This limit, called the Two-Scale Shuffle limit, contains all the information present in all the two-scale limits in the sequence.< Réduire
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