The Laplace Equation Boundary Value Problems on Bounded and Unbounde
This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission p
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The Laplace Equation
Boundary Value Problems on Bounded and Unbounded Lipschitz Domains
The Laplace Equation
Dagmar Medková
The Laplace Equation Boundary Value Problems on Bounded and Unbounded Lipschitz Domains
123
Dagmar Medková Institute of Mathematics of the Czech Academy of Sciences Praha 1, Czech Republic
ISBN 978-3-319-74306-6 ISBN 978-3-319-74307-3 (eBook) https://doi.org/10.1007/978-3-319-74307-3 Library of Congress Control Number: 2018936510 Mathematics Subject Classification (2010): 35J05, 35J25, 35J20, 31-01 © 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 book is devoted to the Laplace equation as one of the most important equations in mathematical physics. Results of the theory of boundary value problems for the Poisson equation are useful in many fields of physics, and also in other mathematical theories—for example, in the theory of boundary value problems for elliptic equations and in hydrodynamics. So, we aimed to write this text to be as accessible as possible to experts in other fields and to research students. In the preliminary chapter, we gather all fundamental definitions and propositions from various fields of mathematics that we use in this book. Boundary value problems for the Laplace equation are studied independently in potential theory, in the theory of partial differential equations, and in harmonic analysis by distinct methods. Here, we attempt to gather the most important results of these theories concerning boundary value problems for the Laplace equation or, more generally, for the Poisson equation. Contain
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