Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit
ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 4, pp. 931-946.

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.

DOI: 10.1051/cocv/2012039
Classification: 35B27
Keywords: homogenization, two-scale convergence
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     title = {Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {931--946},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {4},
     year = {2013},
     doi = {10.1051/cocv/2012039},
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     zbl = {1284.35051},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2012039/}
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Santugini, Kévin. Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 4, pp. 931-946. doi : 10.1051/cocv/2012039. http://www.numdam.org/articles/10.1051/cocv/2012039/

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