Potential Theory
Aimed at graduate students and researchers in mathematics, physics, and engineering, this book presents a clear path from calculus to classical potential theory and beyond, moving the reader into a fertile area of mathematical research as quickly as possi
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Lester L. Helms
Potential Theory
123
Lester L. Helms University of Illinois Department of Mathematics 1409 W. Green St. Urbana IL 61801, USA [email protected]
Editorial board: Sheldon Axler, San Francisco State University Vincenzo Capasso, Università degli Studi di Milano Carles Casacuberta, Universitat de Barcelona Angus MacIntyre, Queen Mary, University of London Kenneth Ribert, University of California, Berkeley Claude Sabbah, CNRS, École Polytechnique Endre Süli, University of Oxford Wojbor Woyczy´nski, Case Western Reserve University
ISBN 978-1-84882-318-1 e-ISBN 978-1-84882-319-8 DOI 10.1007/978-1-84882-319-8 Springer Dordrecht Heidelberg London New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2009926475 Mathematics Subject Classification (2000): 33E30, 35C15, 35J05, 35J15, 35J40, 35J55, 35J67 c Springer-Verlag London Limited 2009 ° Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to my wife Dorothea Helms
Preface
The first six chapters of this book are revised versions of the same chapters in the author’s 1969 book, Introduction to Potential Theory. At the time of the writing of that book, I had access to excellent articles, books, and lecture notes by M. Brelot. The clarity of these works made the task of collating them into a single body much easier. Unfortunately, there is not a similar collection relevant to more recent developments in potential theory. A newcomer to the subject will find the journal literature to be a maze of excellent papers and papers that never should have been published as presented. In the Opinion Column of the August, 2008, issue of the Notices of the American Mathematical Society, M. Nathanson of Lehman College (CUNY) and (CUNY) Graduate Center said it best “...When I read a journal article, I often find mistakes. Whether I can fix them is irrelevant. The litera
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