Variational Methods for Crystalline Microstructure - Analysis and Computation
Phase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, of
- PDF / 3,277,668 Bytes
- 217 Pages / 430.874 x 666.15 pts Page_size
- 104 Downloads / 155 Views
1803
3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo
Georg Dolzmann
Variational Methods for Crystalline Microstructure Analysis and Computation
13
Author Georg Dolzmann Department of Mathematics University of Maryland College Park MD 20742 Maryland, USA e-mail: [email protected] http://www.math.umd.edu/˜dolzmann/
Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 74B20, 74G15, 74G65, 74N15, 65M60 ISSN 0075-8434 ISBN 3-540-00114-X Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2003 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10899540
41/3142/ du - 543210 - Printed on acid-free paper
Preface
The mathematical modeling of microstructures in solids is a fascinating topic that combines ideas from different fields such as analysis, numerical simulation, and materials science. Beginning in the 80s, variational methods have been playing a prominent rˆ ole in modern theories for microstructures, and surprising developments in the calculus of variations were stimulated by questions arising in this context. This text grew out of my Habilitationsschrift at the University of Leizpig, and would not have been possible without the constant support and encouragement of all my friends during the past years. In particular I would like to thank S. M¨ uller for having given me the privilege of being a member of his group during my years in Leipzig in which the bulk of the work was completed. Finally, the financial support through the Max Planck Institute for Mathematics in the Sciences, Leipzig, my home institution, the University of Maryland at College Park, and the NSF through grant DMS0104118 is gratefully acknowledged. College Park, August 20
Data Loading...
