Periodic Homogenization of Elliptic Systems: 269 (Advances in Partial Differential Equations) - Hardcover

Shen, Zhongwei

Hardcover

ISBN 10: 3319912135 ISBN 13: 9783319912134

Verlag: Birkhäuser, 2018

Inhaltsangabe

<P>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&GT;0. ADDITIONAL TOPICS INCLUDE CONVERGENCE RATES FOR DIRICHLET EIGENVALUES AND ASYMPTOTIC EXPANSIONS OF FUNDAMENTAL SOLUTIONS, GREEN FUNCTIONS, AND NEUMANN FUNCTIONS.</P> <P>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.</P>

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Reseña del editor:

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.

Über diese Auflage

• Verlag: Birkhäuser
• Erscheinungsdatum: 2018
• ISBN 10: 3319912135
• ISBN 13: 9783319912134
• Einband: Tapa dura
• Auflage: 1
• Anzahl der Seiten: 304