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Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2013

Homogenization at different linear scales, bounded martingales and the Two-Scale Shuffle limit

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 $\mathrm{L}^2$ 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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Dates and versions

hal-00621265 , version 1 (09-09-2011)
hal-00621265 , version 2 (27-09-2011)
hal-00621265 , version 3 (01-06-2012)
hal-00621265 , version 4 (26-09-2012)

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Kévin Santugini-Repiquet. Homogenization at different linear scales, bounded martingales and the Two-Scale Shuffle limit. ESAIM: Control, Optimisation and Calculus of Variations, 2013, 19, pp.931--946. ⟨10.1051/cocv/2012039⟩. ⟨hal-00621265v4⟩
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