Topics in the Mathematical Modelling of Composite Materials

Over the past several decades, we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous materials. This activity brings together a number of related themes, including: (1) the use of weak convergence

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Andrej V. Cherkaev Robert Kohn Editors

Topics in the Mathematical Modelling of Composite Materials

Modern Birkhäuser Classics Many of the original research and survey monographs, as well as textbooks, in pure and applied mathematics published by Birkhäuser in recent decades have been groundbreaking and have come to be regarded as foundational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain accessible to new generations of students, scholars, and researchers.

Topics in the Mathematical Modelling of Composite Materials Andrej V. Cherkaev Robert Kohn Editors

Reprint of the 1997 Edition

Editors Andrej V. Cherkaev Department of Mathematics University of Utah Salt Lake City, Utah, USA

Robert Kohn Courant Mathematical Institute New York University New York, USA

ISSN 2197-1803 ISSN 2197-1811 (electronic) Modern Birkhäuser Classics ISBN 978-3-319-97183-4 ISBN 978-3-319-97184-1 (eBook) https://doi.org/10.1007/978-3-319-97184-1 Library of Congress Control Number: 2018950852 © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Topics in the Mathematical Modelling of Composite Materials

Andrej Cherkaev

RobertKohn Editors

Springer Science+Business Media, LLC

Andrej Cherkaev Department of Mathematics University of Utah Salt Lake City, UT 84112

Robert Kohn Courant Mathematical Institute New York University New York, NY 10012

Library of Congress Cataloging-in-Publication Data Topics in the mathematical modelling of composite materials / Andrej Cherkaev, Robert Kohn, editor