Corrector estimates for elliptic systems with random periodic coefficients

Abstract

We consider an elliptic system of equations on the torus ${\left[-\frac{L}{2},\frac{L}{2}\right)}^d$ with random coefficients $A$, that are assumed to be coercive and stationary. Using two different approaches we obtain moment bounds on the gradient of the corrector, independent of the domain size $L$. In the first approach we use Green function representation. For that we require $A$ to be locally Hölder continuous and distribution of $A$ to satisfy Logarithmic Sobolev inequality. The second method works for non-smooth (possibly discontinuous) coefficients, and it requires that statistics of $A$ satisfies Spectral Gap estimate.

30 pages

References in corpus (1)

• An optimal error estimate in stochastic homogenization of discrete elliptic equations