Uniform Lipschitz estimates in stochastic homogenization
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
Keywords: 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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