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MiS Preprint
100/2014

Corrector estimates for elliptic systems with random periodic coefficients

Peter Bella and Felix Otto

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 H\"older 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.

Received:
25.09.2014
Published:
01.10.2014

Related publications

inJournal
2016 Repository Open Access
Peter Bella and Felix Otto

Corrector estimates for elliptic systems with random periodic coefficients

In: Multiscale modeling and simulation, 14 (2016) 4, pp. 1434-1462