Hadamard Variation for Electromagnetic Frequencies
A regular variation of a bounded domain in the Euclidean space is considered. The perturbation formula for the eigenvalue of an operator arising in the Maxwell equation under this type of domain variation is given.
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Editor-in-Chief V. Ancona Series Editors P. Cannarsa C. Canuto G. Coletti P. Marcellini G. Patrizio T. Ruggeri E. Strickland A. Verra
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Rolando Magnanini r Shigeru Sakaguchi Angelo Alvino Editors
Geometric Properties for Parabolic and Elliptic PDE’s
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Editors Rolando Magnanini Dipartimento di Matematica “U. Dini” Università di Firenze Firenze, Italy
Angelo Alvino Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Università di Napoli “Federico II” Napoli, Italy
Shigeru Sakaguchi Graduate School of Information Sciences Division of Mathematics Tohoku University Sendai, Japan
ISSN 2281-518X ISSN 2281-5198 (electronic) Springer INdAM Series ISBN 978-88-470-2840-1 ISBN 978-88-470-2841-8 (eBook) DOI 10.1007/978-88-470-2841-8 Springer Milan Heidelberg New York Dordrecht London Library of Congress Control Number: 2012948272 © Springer-Verlag Italia 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The study of geometric properties of partial differential equations has always attracted the interest of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, fun
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