Quantitative Stochastic Homogenization and Large-Scale Regularity

S. Armstrong: Currently Associate Professor at the Courant Institute at NYU. Received his PhD from University of California, Berkeley, in 2009 and previously held positions at Louisiana State University, The University of Chicago, Univ. of Wisconsin-Madison and the University of Paris-Dauphine with the CNRS.T. Kuusi: Currently Professor at the University of Helsinki. He previously held positions at the University of Oulu and Aalto University. Received his PhD from Aalto University in 2007.J.-C. Mourrat: Currently CNRS research scientist at Ecole Normale Supérieure in Paris. Previously held positions at ENS Lyon and EPFL in Lausanne. Received his PhD in 2010 jointly from Aix-Marseille University and PUC in Santiago, Chile.

• Preface.- Assumptions and examples.- Frequently asked questions.- Notation.- Introduction and qualitative theory.- Convergence of the subadditive quantities.- Regularity on large scales.- Quantitative description of first-order correctors.- Scaling limits of first-order correctors.- Quantitative two-scale expansions.- Calderon-Zygmund gradient L^p estimates.- Estimates for parabolic problems.- Decay of the parabolic semigroup.- Linear equations with nonsymmetric coefficients.- Nonlinear equations.- Appendices: A.The O_s notation.- B.Function spaces and elliptic equations on Lipschitz domains.- C.The Meyers L^{2+\delta} estimate.- D. Sobolev norms and heat flow.- Parabolic Green functions.- Bibliography.- Index.

“The text presents a nice collection of important results in the theory of stochastic homogenization and regularity theory. … The text is a very well-written piece of work that is pleasant to read. It is an excellent resource both for experts and beginners in field of stochastic homogenization.” (Alpár R. Mészáros, zbMATH 1482.60001, 2022)