Quantitative Stochastic Homogenization and Large-Scale Regularity [electronic resource] by Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat.

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...

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Bibliographic Details
Uniform Title:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 2196-9701 ; 352
Main Authors: Armstrong, Scott (Author)
Kuusi, Tuomo (Author)
Mourrat, Jean-Christophe (Author)
Corporate Author: SpringerLink (Online service)
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:
Differential equations.
Probabilities.
Mathematical physics.
Mathematical optimization.
Calculus of variations.
Online Access:
Springer Mathematics and Statistics eBooks 2019 English/International: 2019 (Springer Link)
Format: Electronic eBook
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.