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| HAL : hal-00621265, version 3 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (10-09-2011) | v2 (27-09-2011) | v3 (03-06-2012) | v4 (27-09-2012) |
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| Homogenization at different linear scales, bounded martingales and the Two-Scale Shuffle limit |
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| Kévin Santugini-Repiquet 1, 2 |
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| (09/09/2011) |
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| In this paper, we consider two-scale limits obtained with increasing homogenization periods, each period being a 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. |
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| 1 : | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 2 : | MC2 (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00621265, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00621265 | |
| oai:hal.archives-ouvertes.fr:hal-00621265 | |
| Contributeur : Kévin Santugini Repiquet | |
| Soumis le : Vendredi 1 Juin 2012, 22:22:10 | |
| Dernière modification le : Dimanche 3 Juin 2012, 12:52:30 | |
