Modern Aspects of the Theory of Partial Differential Equations
The book provides a quick overview of a wide range of active research areas in partial differential equations such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular
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Editors: Joseph A. Ball (Blacksburg, VA, USA) Harry Dym (Rehovot, Israel) Marinus A. Kaashoek (Amsterdam, The Netherlands) Heinz Langer (Vienna, Austria) Christiane Tretter (Bern, Switzerland) Associate Editors: Vadim Adamyan (Odessa, Ukraine) Albrecht Böttcher (Chemnitz, Germany) B. Malcolm Brown (Cardiff, UK) Raul Curto (Iowa, IA, USA) Fritz Gesztesy (Columbia, MO, USA) Pavel Kurasov (Lund, Sweden) Leonid E. Lerer (Haifa, Israel) Vern Paulsen (Houston, TX, USA) Mihai Putinar (Santa Barbara, CA, USA) Leiba Rodman (Williamsburg, VA, USA) Ilya M. Spitkovsky (Williamsburg, VA, USA)
Subseries Linear Operators and Linear Systems Subseries editors: Daniel Alpay (Beer Sheva, Israel) Birgit Jacob (Wuppertal, Germany) André C.M. Ran (Amsterdam, The Netherlands) Subseries Advances in Partial Differential Equations Subseries editors: Bert-Wolfgang Schulze (Potsdam, Germany) Michael Demuth (Clausthal, Germany) Jerome A. Goldstein (Memphis, TN, USA) Nobuyuki Tose (Yokohama, Japan) Ingo Witt (Göttingen, Germany)
Honorary and Advisory Editorial Board: Lewis A. Coburn (Buffalo, NY, USA) Ciprian Foias (College Station, TX, USA) J.William Helton (San Diego, CA, USA) Thomas Kailath (Stanford, CA, USA) Peter Lancaster (Calgary, Canada) Peter D. Lax (New York, NY, USA) Donald Sarason (Berkeley, CA, USA) Bernd Silbermann (Chemnitz, Germany) Harold Widom (Santa Cruz, CA, USA)
Modern Aspects of the Theory of Partial Differential Equations Michael Ruzhansky Jens Wirth Editors
A P D E
Advances in Partial Differential Equations
Editors Michael Ruzhansky Department of Mathematics Imperial College London 180 Queen’s Gate London SW7 2AZ UK [email protected]
Jens Wirth Department of Mathematics University of Stuttgart Pfaffenwaldring 57 70569 Stuttgart Germany [email protected]
2010 Mathematics Subject Classification: 35-06, 35Jxx, 35Kxx, 35Lxx, 35Pxx, 35Sxx, 31A25, 45K05, 45Q05, 47B35, 65E05, 65Nxx ISBN 978-3-0348-0068-6 e-ISBN 978-3-0348-0069-3 DOI 10.1007/978-3-0348-0069-3 Library of Congress Control Number: 2011928227 © Springer Basel AG 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. Cover design: deblik, Berlin Printed on acid-free paper Springer Basel AG is part of Springer Science+Business Media www.birkhauser-science.com
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
L. Boutet de Monvel Toeplitz Operators and Asymptotic Equivariant Index . . . . . . . . . . . . . .
1
V. Kokilashvili Boundary Value Problems of Analytic and Harmonic Functions in a Domain with Piecewise Smooth Boundary in the Frame of Variable Exponent Lebesgue Spaces . . . . . . . . . . . . . . . . . . . . .
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