Stationary Diffraction by Wedges Method of Automorphic Functions on
This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different ar
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Alexander Komech Anatoli Merzon
Stationary Diffraction by Wedges
Method of Automorphic Functions on Complex Characteristics
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Editors: Karin Baur, Leeds Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Annette Huber, Freiburg Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Cambridge Angela Kunoth, Cologne Ariane Mézard, Paris Mark Podolskij, Aarhus Sylvia Serfaty, New York Gabriele Vezzosi, Firenze Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Alexander Komech • Anatoli Merzon
Stationary Diffraction by Wedges Method of Automorphic Functions on Complex Characteristics
123
Alexander Komech Faculty of Mathematics University of Vienna Vienna, Austria
Anatoli Merzon Instituto de Fisica y Matematicas Universidad Michoacana de San Nicolas de Hidalgo Morelia Michoacán, Mexico
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-030-26698-1 ISBN 978-3-030-26699-8 (eBook) https://doi.org/10.1007/978-3-030-26699-8 Mathematics Subject Classification (2010): Primary: 35J25, 78A45; Secondary: 35Q60 © Springer Nature Switzerland AG 2019 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
To the blessed memory of Nina Ilina
Preface
We present a complete solution to the classical problem of stationary diffraction by wedges with general boundary conditions (b.c.). For the Dirichlet and Neumann b.c., the solution was found by Sommerfeld in 1896 and for the impedance b.c. (or Leontovich and Robin b.c.) by Malyuzhinetz in 1958. Our approach relies on a novel “method of automo
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