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Periodic Homogenization of Elliptic Systems

  • Zhongwei Shen

Part of the Operator Theory: Advances and Applications book series (OT, volume 269)

Also part of the Advances in Partial Differential Equations book sub series (APDE, volume 269)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Zhongwei Shen
    Pages 1-6
  3. Zhongwei Shen
    Pages 33-63
  4. Zhongwei Shen
    Pages 65-97
  5. Zhongwei Shen
    Pages 99-134
  6. Zhongwei Shen
    Pages 135-168
  7. Zhongwei Shen
    Pages 169-203
  8. Zhongwei Shen
    Pages 205-281
  9. Back Matter
    Pages 283-291

About this book

Introduction

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.

Keywords

homogenization elliptic systems, convergence rates periodic coefficients boundary value problems regularity estimates layer potentials

Authors and affiliations

  • Zhongwei Shen
    • 1
  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-91214-1
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-91213-4
  • Online ISBN 978-3-319-91214-1
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site