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Scott Armstrong
Uniform Lipschitz estimates in stochastic homogenization
Journées équations aux dérivées partielles (2014), Exp. No. 1, 11 p., doi: 10.5802/jedp.104
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Class. Math.: 35B27, 60H25, 35J20, 35J62
Mots clés: Stochastic homogenization, Lipschitz regularity, error estimate

Résumé - Abstract

We review some recent results in quantitative stochastic homogenization for divergence-form, quasilinear elliptic equations. In particular, we are interested in obtaining $L^\infty $-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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