# Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 4, page 931-946
- ISSN: 1292-8119

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topSantugini, Kévin. "Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit." ESAIM: Control, Optimisation and Calculus of Variations 19.4 (2013): 931-946. <http://eudml.org/doc/272787>.

@article{Santugini2013,

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 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.},

author = {Santugini, Kévin},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {homogenization; two-scale convergence; sequence of two-scale limits},

language = {eng},

number = {4},

pages = {931-946},

publisher = {EDP-Sciences},

title = {Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit},

url = {http://eudml.org/doc/272787},

volume = {19},

year = {2013},

}

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

PB - EDP-Sciences

VL - 19

IS - 4

SP - 931

EP - 946

AB - 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.

LA - eng

KW - homogenization; two-scale convergence; sequence of two-scale limits

UR - http://eudml.org/doc/272787

ER -

## References

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