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Françoise Demengel Gilbert Demengel

Functional Spaces for the Theory of Elliptic Partial Differential Equations

Universitext

Universitext Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Vincenzo Capasso Università degli Studi di Milano, Milan, Italy Carles Casacuberta Universitat de Barcelona, Barcelona, Spain Angus J. MacIntyre Queen Mary, University of London, London, UK Kenneth Ribet University of California, Berkeley, Berkeley, CA, USA Claude Sabbah CNRS, École Polytechnique, Palaiseau, France Endre Süli University of Oxford, Oxford, UK Wojbor A. Woyczynski Case Western Reserve University, Cleveland, OH, USA

Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal, even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, into very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext.

For further volumes: www.springer.com/series/223

Françoise Demengel r Gilbert Demengel

Functional Spaces for the Theory of Elliptic Partial Differential Equations Translated by Reinie Erné

Françoise Demengel Département de Mathématiques Université de Cergy-Pontoise Cergy-Pontoise Cedex, France

Gilbert Demengel Paris Cedex 13, France

Translator Reinie Erné Leiden, The Netherlands

Translation from the French language edition: Espaces fonctionnels: Utilisation dans la résolution des équations aux dérivées partielles by Françoise Demengel & Gilbert Demengel EDP Sciences ISBN 978-2-7598-0698-0 Copyright © 2007 EDP Sciences, CNRS Editions, France. http://www.edpsciences.org/ http://www.cnrseditions.fr/ All Rights Reserved ISSN 0172-5939 e-ISSN 2191-6675 Universitext ISBN 978-1-4471-2806-9 e-ISBN 978-1-4471-2807-6 DOI 10.1007/978-1-4471-2807-6 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2012931004 Mathematics Subject Classification: 35J05, 35J15, 35J25, 35J40, 35J55, 35J70, 42A85, 42C05, 46F05, 46F10, 46E27, 46E30, 46E35, 49R50 © Springer-Verlag London Limited 2012 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered