WIAS Preprint No. 1836, (2013)

Moment bounds for the corrector in stochastic homogenization of a percolation model



Authors

  • Lamacz, Agnes
  • Neukamm, Stefan
  • Otto, Felix

2010 Mathematics Subject Classification

  • 35B27 60K37 60F99 60H25 39A70

Keywords

  • stochastic homogenization, percolation, corrector equation, quantitative results

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 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 by Gloria and the third author, 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.

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