Vector-Valued Partial Differential Equations and Applications Cetrar

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Ma

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Bernard Dacorogna · Nicola Fusco Stefan Müller · Vladimir Sverak

Vector-Valued Partial Differential Equations and Applications Cetraro, Italy 2013 John Ball · Paolo Marcellini Editors

Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zurich Mario Di Bernardo, Bristol Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg

More information about this series at http://www.springer.com/series/304

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Bernard Dacorogna • Nicola Fusco • Stefan MRuller • Vladimir Sverak

Vector-Valued Partial Differential Equations and Applications Cetraro, Italy 2013 John Ball • Paolo Marcellini Editors

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Authors Bernard Dacorogna Section de Mathématiques, EPFL Lausanne, Switzerland

Nicola Fusco Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Università degli Studi di Napoli “Federico II” Napoli, Italy

Stefan MRuller Hausdorff Center for Mathematics & Department of Applied Mathematics University of Bonn Bonn, Germany

Editors John Ball Mathematical Institute University of Oxford Oxford, United Kingdom

ISSN 0075-8434 Lecture Notes in Mathematics C.I.M.E. Foundation Subseries ISBN 978-3-319-54513-4 DOI 10.1007/978-3-319-54514-1

Vladimir Sverak School of Mathematics University of Minnesota Minneapolis, MN, USA

Paolo Marcellini Dipartimento di Matematica UniversitJa di Firenze Firenze, Italy

ISSN 1617-9692 (electronic) ISBN 978-3-319-54514-1 (eBook)

Library of Congress Control Number: 2017940495 Mathematics Subject Classification (2010): 49-XX, 35-XX, 35QXX © Springer International Publishing AG 2017 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The regi