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arXiv · 1705.05300

Quantitative stochastic homogenization and large-scale regularity

Scott Armstrong·Tuomo Kuusi·Jean-Christophe Mourrat
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Abstract

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. There are several chapters containing new results, such as: quantitative estimates for the Dirichlet problem, including optimal quantitative estimates of the homogenization error and the two-scale expansion; optimal estimates for the homogenization of the parabolic and elliptic Green functions; and $W^{1,p}$-type estimates for two-scale expansions.

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Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat. 2017-05-15. Quantitative stochastic homogenization and large-scale regularity. https://doi.org/10.1007/978-3-030-15545-2

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