Homogenization at different linear scales and bounded martingales
Kévin Santugini-Repiquet · 2011
In this short paper, we look at two scale limits of sequences with varying 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 $L^2$ and almost everywhere when the period tend to $+\infty$. This limit contains all the information present in all the two scale limits in the sequence.