The focus of this book is the large-scale statistical behavior of solutions of divergence-form
elliptic equations with random coefficients, which is closely related to the long-time …

Periodic Homogenization of Elliptic Systems Page 1 Operator Theory Advances and
Applications 269 Zhongwei Shen Periodic Homogenization of Elliptic Systems Page 2 Page 3 …

One of the principal difficulties in stochastic homogenization is transferring quantitative
ergodic information from the coefficients to the solutions, since the latter are nonlocal …

Since the seminal results by Avellaneda & Lin it is known that elliptic operators with periodic
coefficients enjoy the same regularity theory as the Laplacian on large scales. In a recent …

Since the seminal results by Avellaneda\& Lin it is known that elliptic operators with periodic
coefficients enjoy the same regularity theory as the Laplacian on large scales. In a recent …

This paper is about the homogenization of linear elliptic operators in divergence form with
stationary random coefficients that have only slowly decaying correlations. It deduces …

We give a self-contained introduction of the theory of elliptic homogenization for random
coefficient fields, starting from classical qualitative homogenization. Our exposition of the …

Four quantities are fundamental in homogenization of elliptic systems in divergence form
and in its applications: the field and the flux of the solution operator (applied to a general …

We study Coulomb gases in any dimension d\geq2 and in a broad temperature regime. We
prove local laws on the energy, separation and number of points down to the microscopic …

We establish quantitative homogenization, large‐scale regularity, and Liouville results for
the random conductance model on a supercritical (Bernoulli bond) percolation cluster. The …