Partial Differential Equations
This textbook is intended for students who wish to obtain an introduction to the theory of partial di?erential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not o?er a comprehensive overview of the whole ?eld of PDEs, b
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Editorial Board: S. Axler Mathematics Department San Francisco State University San Francisco, CA 94132 USA [email protected]
F.W. Gehring Mathematics Department East Hall University of Michigan Ann Arbor, MI 48109 USA [email protected]
K.A. Ribet Mathematics Department University of California, Berkeley Berkeley, CA 94720-3840 USA [email protected]
Mathematics Subject Classification (2000): 35-01, 35Jxx, 35Kxx, 35Axx, 35Bxx Library of Congress Cataloging-in-Publication Data Jost, Ju¨rgen, 1956– Partial differential equations/Ju¨rgen Jost. p. cm. — (Graduate texts in mathematics; 214) Includes bibliographical references and index. ISBN 0-387-95428-7 (hardcover: alk. paper) 1. Differential equations, Partial. I. Title. II. Series. QA377 .J66 2002 515′.353—dc21 2001059798 ISBN 0-387-95428-7
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This book is an expanded translation of the original German version, Partielle Differentialgleichungen, published by Springer-Verlag Heidelberg in 1998. © 2002 Springer-Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1
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Preface
This textbook is intended for students who wish to obtain an introduction to the theory of partial differential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not offer a comprehensive overview of the whole field of PDEs, but tries to lead the reader to the most important methods and central results in the case of elliptic PDEs. The guiding question is how one can find a solution of such a PDE. Such a solution will, of course, depend on given constraints and, in turn, if the constraints are of the appropriate type, be uniquely determined by them. We shall pursue a number of strategies for finding a solution of a PDE; they can be informally characterized as follows: (0) Write down an explicit formula for the solution in terms of the given data (constraints). This may seem like the best and most natural approach, but this is possible only in rather particular and special cases. Also, such a formula may be rather complicated, so that it is not very helpful for detecting q
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