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The Resource Quantitative Stochastic Homogenization and Large-Scale Regularity, by Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat, (electronic resource)

Quantitative Stochastic Homogenization and Large-Scale Regularity, by Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat, (electronic resource)

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Author
Contributor
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.
Language
eng
Work
Publication
Edition
1st ed. 2019.
Extent
XXXVIII, 518 p. 430 illus., 4 illus. in color.
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
Isbn
9783030155452
Instance
Label
Quantitative Stochastic Homogenization and Large-Scale Regularity
Title
Quantitative Stochastic Homogenization and Large-Scale Regularity
Statement of responsibility
by Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat
Creator
Contributor
Author
Author
Subject
Language
eng
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.
Member of
Is part of
http://library.link/vocab/creatorName
Armstrong, Scott
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • Q7Q74SGXPO0
  • keJE7yjSh7M
  • bOVIAynwz18
Image bit depth
0
LC call number
QA370-380
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Kuusi, Tuomo.
  • Mourrat, Jean-Christophe.
Series statement
Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
Series volume
352
http://library.link/vocab/subjectName
  • Differential equations, Partial
  • Probabilities
  • Mathematical physics
  • Calculus of variations
  • Partial Differential Equations
  • Probability Theory and Stochastic Processes
  • Mathematical Physics
  • Calculus of Variations and Optimal Control; Optimization
Label
Quantitative Stochastic Homogenization and Large-Scale Regularity, by Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Edition
1st ed. 2019.
Extent
XXXVIII, 518 p. 430 illus., 4 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783030155452
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-030-15545-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-030-15545-2
Label
Quantitative Stochastic Homogenization and Large-Scale Regularity, by Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Edition
1st ed. 2019.
Extent
XXXVIII, 518 p. 430 illus., 4 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783030155452
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-030-15545-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-030-15545-2

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