Partial Differential Equations and Geometric Measure Theory Cetraro,

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory.  It features a wide variety of research topics in which a crucial role is played by the interaction of fine analy

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Alessio Figalli · Ireneo Peral Enrico Valdinoci

Partial Differential Equations and Geometric Measure Theory Cetraro, Italy 2014 Alberto Farina · Enrico Valdinoci Editors

Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zurich 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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Alessio Figalli • Ireneo Peral • Enrico Valdinoci

Partial Differential Equations and Geometric Measure Theory Cetraro, Italy 2014 Alberto Farina • Enrico Valdinoci Editors

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Authors Alessio Figalli Department of Mathematics ETH Zurich Zurich, Switzerland

Ireneo Peral Departamento de Matemáticas Universidad Autónoma de Madrid Madrid, Spain

Enrico Valdinoci Dipartimento di Matematica Università di Milano Milano, Italy Editors Alberto Farina LAMFA University of Picardie at Amiens Amiens, France

Enrico Valdinoci Dipartimento di Matematica Università di Milano Milano, Italy

ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics C.I.M.E. Foundation Subseries ISBN 978-3-319-74041-6 ISBN 978-3-319-74042-3 (eBook) https://doi.org/10.1007/978-3-319-74042-3 Library of Congress Control Number: 2018935159 Mathematics Subject Classification (2010): 35J15, 26A33, 35R35 © Springer International Publishing AG, part of Springer Nature 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. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Introduction

This collection of notes consists o