Quantitative Stochastic Homogenization and Large-Scale Regularity

By S. Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat. Grundlehren der mathematischen Wissenschaften, 2017

244 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b2b852e07d14a42d0bc13191a8ac0ca49c9beeae

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A Regularity Theory for Random Elliptic Operators (2014, methodology): “Between the first posted version [39] and the current version of this paper, Armstrong and Mourrat [4], and subsequently Armstrong, Mourrat and Kuusi [6, 7, 8] significantly extended the regularity theory of [5] in several directions: First, using the framework of the Fitzpatrick duality theory, the”