Free Boundary Problems Regularity Properties Near the Fixed Boundary
This book is concerned with several elliptic and parabolic obstacle-type problems with a focus on the cases where the free and fixed boundaries meet. The results presented complement those found in existing books in the subject, which mainly treat regular
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Darya Apushkinskaya
Free Boundary Problems Regularity Properties Near the Fixed Boundary
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Darya Apushkinskaya
Free Boundary Problems Regularity Properties Near the Fixed Boundary
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Darya Apushkinskaya Department of Mathematics Saarland University Saarbr¨ucken Germany
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-97078-3 ISBN 978-3-319-97079-0 (eBook) https://doi.org/10.1007/978-3-319-97079-0 Library of Congress Control Number: 2018952878 Mathematics Subject Classification (2010): Primary: 35R35; Secondary: 35R37, 35B65, 35K10, 35J15 © Springer Nature Switzerland AG 2018 Translation from the English language edition: Free Boundary Problems: Regularity Properties Near the Fixed Boundary by Darya Apushkinskaya, Copyright © Springer International Publishing AG, part of Springer Nature 2018. All Rights Reserved. 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. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Free boundary problems (FBPs) belong to the most striking component of the modern theory of partial differential equations (PDEs). The expression FBP refers to a problem in which one or several variables are governed in different subdomains of the space, or space-time, by the different state laws. These subdomains are a priori unknown and have to be determined
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