Periodic homogenization of elliptic systems /

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Bibliographic Details
Author / Creator:	Shen, Zhongwei, 1963- author.
Imprint:	Cham, Switzerland : Birkhäuser, 2018.
Description:	1 online resource
Language:	English
Series:	Operator theory: advances in applications, 2504-3587 ; volume 269 Operator theory, advances and applications ; v. 269.
Subject:	Homogenization (Differential equations) Differential equations, Elliptic -- Numerical solutions. Differential equations, Elliptic -- Numerical solutions. Homogenization (Differential equations)
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11705971

Hidden Bibliographic Details
ISBN:	9783319912141 3319912143 9783319912134 3319912135
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed September 17, 2018).
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.--
Other form:	Print version: Shen, Zhongwei, 1963- Periodic homogenization of elliptic systems. Cham, Switzerland : Birkhäuser, 2018 3319912135 9783319912134

Table of 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

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