Moment bounds for the corrector in stochastic homogenization of a percolation model
Loading...
Date
2013-09-30
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We study the corrector equation in stochastic homogenization for a simplified Bernoulli
percolation model on Z^d, d > 2. The model is obtained from the classical {0,1}-Bernoulli
bond percolation by conditioning all bonds parallel to the first coordinate direction to be
open. As a main result we prove (in fact for a slightly more general model) that stationary
correctors exist and that all finite moments of the corrector are bounded. This extends a
previous result in [8], where uniformly elliptic conductances are treated, to the degenerate
case. Our argument is based on estimates on the gradient of the elliptic Green's function.