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arXiv · 1207.6077

Strong Convergence to the homogenized limit of elliptic equations with random coefficients II

Joseph G. Conlon·Arash Fahim
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Abstract

Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice $\Z^d$ with random coefficients. In [3] rate of convergence results in homogenization and estimates on the difference between the averaged Green's function and the homogenized Green's function for random environments which satisfy a Poincaré inequality were obtained. Here these results are extended to certain environments with long range correlations. These environments are simply related via a convolution to environments which do satisfy a Poincaré inequality.

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Joseph G. Conlon, Arash Fahim. 2012-07-25. Strong Convergence to the homogenized limit of elliptic equations with random coefficients II. https://doi.org/10.1112/blms%2Fbdt025

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