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Uniform Lipschitz estimates in stochastic homogenization

Scott Armstrong (2014)

Journées Équations aux dérivées partielles

We review some recent results in quantitative stochastic homogenization for divergence-form, quasilinear elliptic equations. In particular, we are interested in obtaining L -type bounds on the gradient of solutions and thus giving a demonstration of the principle that solutions of equations with random coefficients have much better regularity (with overwhelming probability) than a general equation with non-constant coefficients.

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