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The Resource Periodic homogenization of elliptic systems, Zhongwei Shen

Periodic homogenization of elliptic systems, Zhongwei Shen

Label
Periodic homogenization of elliptic systems
Title
Periodic homogenization of elliptic systems
Statement of responsibility
Zhongwei Shen
Creator
Author
Subject
Language
eng
Summary
This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.--
Member of
Assigning source
Provided by publisher
Cataloging source
N$T
http://library.link/vocab/creatorDate
1963-
http://library.link/vocab/creatorName
Shen, Zhongwei
Dewey number
515/.35
Index
index present
LC call number
QA377
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Operator theory: advances in applications,
Series volume
volume 269
http://library.link/vocab/subjectName
  • Homogenization (Differential equations)
  • Differential equations, Elliptic
Label
Periodic homogenization of elliptic systems, Zhongwei Shen
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Contents; Preface; Chapter 1 Introduction; 1.1 Homogenization theory; 1.2 General presentation of the monograph; Qualitative homogenization theory; Convergence rates; Interior and boundary regularity estimates; The problem of convergence rates revisited; L2 boundary value problems in Lipschitz domains; 1.3 Readership; 1.4 Notation; Chapter 2 Second-Order Elliptic Systems with Periodic Coefficients; 2.1 Weak solutions; 2.2 Two-scale asymptotic expansions and the homogenized operator; Correctors and effective coefficients; 2.3 Homogenization of elliptic systems
  • 6.4 Boundary Lipschitz estimates6.5 Matrix of Neumann functions; 6.6 Elliptic systems of linear elasticity; 6.7 Notes; Chapter 7 Convergence Rates, Part II; 7.1 Convergence rates in H1 and L2; 7.2 Convergence rates of eigenvalues; 7.3 Asymptotic expansions of Green functions; 7.4 Asymptotic expansions of Neumann functions; 7.5 Convergence rates in Lp and W1,p; 7.6 Notes; Chapter 8 L2 Estimates in Lipschitz Domains; 8.1 Lipschitz domains and nontangential convergence; 8.2 Estimates of fundamental solutions; 8.3 Estimates of singular integrals; 8.4 The method of layer potentials
  • 8.5 Laplace's equation8.6 The Rellich property; 8.7 The well-posedness for the small scale; 8.8 Rellich estimates for the large scale; 8.9 L2 boundary value problems; 8.10 L2 estimates in arbitrary Lipschitz domains; 8.11 Square function and H1/2 estimates; 8.12 Notes; Bibliography; Index
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319912134
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
Label
Periodic homogenization of elliptic systems, Zhongwei Shen
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Contents; Preface; Chapter 1 Introduction; 1.1 Homogenization theory; 1.2 General presentation of the monograph; Qualitative homogenization theory; Convergence rates; Interior and boundary regularity estimates; The problem of convergence rates revisited; L2 boundary value problems in Lipschitz domains; 1.3 Readership; 1.4 Notation; Chapter 2 Second-Order Elliptic Systems with Periodic Coefficients; 2.1 Weak solutions; 2.2 Two-scale asymptotic expansions and the homogenized operator; Correctors and effective coefficients; 2.3 Homogenization of elliptic systems
  • 6.4 Boundary Lipschitz estimates6.5 Matrix of Neumann functions; 6.6 Elliptic systems of linear elasticity; 6.7 Notes; Chapter 7 Convergence Rates, Part II; 7.1 Convergence rates in H1 and L2; 7.2 Convergence rates of eigenvalues; 7.3 Asymptotic expansions of Green functions; 7.4 Asymptotic expansions of Neumann functions; 7.5 Convergence rates in Lp and W1,p; 7.6 Notes; Chapter 8 L2 Estimates in Lipschitz Domains; 8.1 Lipschitz domains and nontangential convergence; 8.2 Estimates of fundamental solutions; 8.3 Estimates of singular integrals; 8.4 The method of layer potentials
  • 8.5 Laplace's equation8.6 The Rellich property; 8.7 The well-posedness for the small scale; 8.8 Rellich estimates for the large scale; 8.9 L2 boundary value problems; 8.10 L2 estimates in arbitrary Lipschitz domains; 8.11 Square function and H1/2 estimates; 8.12 Notes; Bibliography; Index
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319912134
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote

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