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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.
@article{COCV_2013__19_4_931_0,
author = {Santugini, K\'evin},
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},
mrnumber = {3182675},
zbl = {1284.35051},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012039/}
}
TY - JOUR AU - Santugini, Kévin TI - Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 931 EP - 946 VL - 19 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012039/ DO - 10.1051/cocv/2012039 LA - en ID - COCV_2013__19_4_931_0 ER -
%0 Journal Article %A Santugini, Kévin %T Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 931-946 %V 19 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012039/ %R 10.1051/cocv/2012039 %G en %F COCV_2013__19_4_931_0
Santugini, Kévin. Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 931-946. doi: 10.1051/cocv/2012039
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