Quantitative stochastic homogenization of convex integral functionals

Abstract

We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched $C^{0,1}$ estimates for local minimizers of such energy functionals.

59 pages, revised version

References in corpus (3)

• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• Correlation structure of the corrector in stochastic homogenization
• Noise-stability and central limit theorems for effective resistance of random electric networks

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• Pointwise two-scale expansion for parabolic equations with random coefficients
• Lipschitz estimates in almost-periodic homogenization
• Eigenvalue fluctuations for random elliptic operators in homogenization regime
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