Overview
- Provides a clear and concise exposition of an important and active area
- Contains a review of the classical theory of qualitative homogenization, and addresses the problem of convergence rates of solutions
- Includes convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions
Part of the book series: Operator Theory: Advances and Applications (OT, volume 269)
Part of the book sub series: Advances in Partial Differential Equations (APDE)
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Table of contents (8 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Periodic Homogenization of Elliptic Systems
Authors: Zhongwei Shen
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-319-91214-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-91213-4Published: 14 September 2018
Softcover ISBN: 978-3-030-08199-7Published: 24 January 2019
eBook ISBN: 978-3-319-91214-1Published: 04 September 2018
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: IX, 291
Topics: Partial Differential Equations, Probability Theory and Stochastic Processes