Type: Article
Publication Date: 2017-10-03
Citations: 102
DOI: https://doi.org/10.4171/jems/745
We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions d \geq 2 . In previous works we studied the model problem of a discrete elliptic equation on \mathbb Z^d . Under the assumption that a spectral gap estimate holds in probability, we proved that there exists a stationary corrector field in dimensions d > 2 and that the energy density of that corrector behaves as if it had finite range of correlation in terms of the variance of spatial averages – the latter decays at the rate of the central limit theorem. In this article we extend these results, and several other estimates, to the case of a continuum linear elliptic equation whose (not necessarily symmetric) coefficient field satisfies a continuum version of the spectral gap estimate. In particular, our results cover the example of Poisson random inclusions.