Quantitative Stochastic Homogenization and Large-Scale Regularity

• Main Authors: Armstrong, Scott (Author, http://id.loc.gov/vocabulary/relators/aut), Kuusi, Tuomo (http://id.loc.gov/vocabulary/relators/aut), Mourrat, Jean-Christophe (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 352
• Subjects: Partial differential equations.; Probabilities.; Mathematical physics.; Calculus of variations.; Partial Differential Equations.; Probability Theory and Stochastic Processes.; Mathematical Physics.; Calculus of Variations and Optimal Control; Optimization.

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 asymptotics of reversible diffusions in random media and other basic models of statistical physics. Of particular inte...

Table of Contents:

• 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.