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Pré-Publication, Document De Travail Année : 2018

Quantitative stochastic homogenization and large-scale regularity

Tuomo Kuusi
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Résumé

This is a preliminary version of a book which presents the quantitative homogenization and large-scale regularity theory for elliptic equations in divergence-form. The self-contained presentation gives new and simplified proofs of the core results proved in the last several years, including the algebraic convergence rate for the variational subadditive quantities, the large-scale Lipschitz and higher regularity estimates and Liouville-type results, optimal quantitative estimates on the first-order correctors and their scaling limit to a Gaussian free field. The last chapter contains new results on the homogenization of the Dirichlet problem, including optimal quantitative estimates of the homogenization error and the two-scale expansion.

Dates et versions

hal-01728747 , version 1 (12-03-2018)

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Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat. Quantitative stochastic homogenization and large-scale regularity. 2018. ⟨hal-01728747⟩
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