Partial Differential Equations VI Elliptic and Parabolic Operators
0. 1. The Scope of the Paper. This article is mainly devoted to the oper ators indicated in the title. More specifically, we consider elliptic differential and pseudodifferential operators with infinitely smooth symbols on infinitely smooth closed manifo
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Editor-in-Chief: R. V. Gamkrelidze
Yu.V. Egorov M.A. Shubin (Eds.)
Partial Differential Equations VI Elliptic and Parabolic Operators
Springer-Verlag Berlin Heidelberg GmbH
Consulting Editors of the Series: AA Agrachev, AA Gonchar, E.F. Mishchenko, N. M. Ostianu, V. P. Sakharova, A B. Zhishchenko
Title of the Russian edition: Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamental'nye napravleniya, VoI. 63, Differentsial'nye uravneniya s chastnymi proizvodnymi 6 Publisher VINITI, Moscow 1990
Mathematics Subject Classification (1991): 35Jxx, 35J55, 35Kxx, 35Sxx, 58G03, 58G15
ISBN 978-3-642-08117-0 ISBN 978-3-662-09209-5 (eBook) DOI 10.1007/978-3-662-09209-5 Cip data applied for This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concemed, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1994 Originally published by Springer-Verlag Berlin Heidelberg New York in 1994 Softcover reprint of the hardcover 1st edition 1994
SPIN: 10020206
41/3140 - 5 4 3 2 l O - Printed on acid-free paper
List of Editors, Authors and Translators Editor-in-Chief R.V. Gamkrelidze, Russian Academy of Sciences, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Institute for Scientific Information (VINITI), ul. Usievicha 20a, 125219 Moscow, Russia, CIS
Consulting Editors Yu. V. Egorov, Moscow State University, Leninskie Gory, 119899 Moscow, Russia, CIS M. A. Shubin, Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119899 Moscow, Russia, CIS
Authors M. S. Agranovich, Moscow Polytechnical Institute, Chair of Algebra and Analysis, Bolshoj Vuzovskij 3/12, 109028 Moscow, Russia, CIS S.D. Ejdel'man, Kiev Institute of Radio-Engineering, 81 Mel'nikov Str., 252064 Kiev, Ukraina, CIS S. Z. Levendorskij, Rostov Institute of National Economy, 69 Engels Str., 344709 Rostov-Don, Russia, CIS B. Paneah, Department of Mathematics, Technion, 32000 Haifa, Israel
Translators M. Capinski, Institute of Mathematics, Jagiellonian University, 30-059 Krakow, ul. Reymonta 4, Poland R. Cooke, Department of Mathematics and Statistics, University of Vermont, 500 South Union Street, Burlington, VT 05401, USA
Contents I. Elliptic Operators on Closed Manifolds M.S. Agranovich 1
II. Degenerate Elliptic Equations and Boundary Problems S. Z. Levendorskij, B. Paneah
131
III. Parabolic Equations S. D. Ejdel'man
203 Author Index
317 Subject Index
321
I. Elliptic Operators on Closed Manifolds M. S. Agranovich Translated from the Russian by M. Gapinski
Contents Preface .
