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January 2022
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Séminaire du LJLL : S. Armstrong
30 janvier 2015 — 14h00
Scott Armstrong (Université Paris Dauphine)
Higher regularity and quantitative results in stochastic homogenization
Abstract
I will review some recent results in the quantitative theory of stochastic homogenization of (linear and nonlinear) elliptic equations in divergence form and explain how the central issue is developing a "higher" regularity theory, that is, showing that equations with random coefficients admit essentially Lipschitz estimates, which is much better than general equations with measurable coefficients. In other words, we show that coefficients for which the De Giorgi-Nash-Moser and Meyers estimates are sharp are not generic. The proof of this result relies on variational methods and a quantitative H-convergence argument.