Uniform Lipschitz estimates in stochastic homogenization
Armstrong, Scott1
1 Ceremade (UMR CNRS 7534) Université Paris-Dauphine Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France
Journées équations aux dérivées partielles (2014), article no. 1, 11 p.

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.

DOI : 10.5802/jedp.104
Classification : 35B27, 60H25, 35J20, 35J62
Mots-clés : Stochastic homogenization, Lipschitz regularity, error estimate
Armstrong, Scott 1

1 Ceremade (UMR CNRS 7534) Université Paris-Dauphine Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16, France 
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Armstrong, Scott. Uniform Lipschitz estimates in stochastic homogenization. Journées équations aux dérivées partielles (2014), article  no. 1, 11 p. doi : 10.5802/jedp.104. http://www.numdam.org/articles/10.5802/jedp.104/

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