Quantitative stochastic homogenization and large-scale regularity /

Quantitative stochastic homogenization and large-scale regularity /

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Bibliographic Details
Author / Creator:Armstrong, Scott, author.
Imprint:Cham, Switzerland : Springer, 2019.
Description:1 online resource
Language:English
Series:Grundlehren der mathematischen Wissenschaften ; volume 352
Grundlehren der mathematischen Wissenschaften ; v. 352.
Subject:
Homogenization (Differential equations)
Homogenization (Differential equations)
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11895309
Hidden Bibliographic Details
Other authors / contributors:Kuusi, Tuomo, author.
Mourrat, Jean-Christophe, author.
ISBN:9783030155452
3030155455
3030155447
9783030155445
9783030155469
3030155463
9783030155476
3030155471
9783030155445
Digital file characteristics:text file
PDF
Notes:Online resource; title from PDF file page (EBSCO, viewed May 13, 2019).
Summary: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 interest is the quantification of the rate at which solutions converge to those of the limiting, homogenized equation in the regime of large scale separation, and the description of their fluctuations around this limit. This self-contained presentation gives a complete account of the essential ideas and fundamental results of this new theory of quantitative stochastic homogenization, including the latest research on the topic, and is supplemented with many new results. The book serves as an introduction to the subject for advanced graduate students and researchers working in partial differential equations, statistical physics, probability and related fields, as well as a comprehensive reference for experts in homogenization. Being the first text concerned primarily with stochastic (as opposed to periodic) homogenization and which focuses on quantitative results, its perspective and approach are entirely different from other books in the literature.
Other form:Printed edition: 9783030155445
Printed edition: 9783030155469
Printed edition: 9783030155476
Standard no.:10.1007/978-3-030-15545-2
10.1007/978-3-030-15
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.

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