Sobolev Spaces in Mathematics II Applications in Analysis and Partia
Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are in the focus of this volume: bound
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SOBOLEV SPACES IN MATHEMATICS II Applications in Analysis and Partial Differential Equations Vladimir Maz’ya EDITOR
SOBOLEV SPACES IN MATHEMATICS II APPLICATIONS IN ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS
INTERNATIONAL MATHEMATICAL SERIES Series Editor: Tamara Rozhkovskaya Novosibirsk, Russia
1. Nonlinear Problems in Mathematical Physics and Related Topics I. In Honor of Professor O.A. Ladyzhenskaya • M.Sh. Birman, S. Hildebrandt, V.A. Solonnikov, N.N. Uraltseva Eds. • 2002 2. Nonlinear Problems in Mathematical Physics and Related Topics II. In Honor of Professor O.A. Ladyzhenskaya • M.Sh. Birman, S. Hildebrandt, V.A. Solonnikov, N.N. Uraltseva Eds. • 2003 3. Different Faces of Geometry • S. Donaldson, Ya. Eliashberg, M. Gromov Eds. • 2004 4. Mathematical Problems from Applied Logic I. Logics for the XXIst Century • D. Gabbay, S. Goncharov, M. Zakharyaschev Eds. • 2006 5. Mathematical Problems from Applied Logic II. Logics for the XXIst Century • D. Gabbay, S. Goncharov, M. Zakharyaschev Eds. • 2007 6. Instability in Models Connected with Fluid Flows I • C. Bardos, A. Fursikov Eds. • 2008 7. Instability in Models Connected with Fluid Flows II • C. Bardos, A. Fursikov Eds. • 2008 8. Sobolev Spaces in Mathematics I. Sobolev Type Inequalities • V. Maz’ya Ed. • 2009 9. Sobolev Spaces in Mathematics II. Applications in Analysis and Partial Differential Equations • V. Maz’ya Ed. • 2009 10. Sobolev Spaces in Mathematics III. Applications in Mathematical Physics • V. Isakov Ed. • 2009
SOBOLEV SPACES IN MATHEMATICS II Applications in Analysis and Partial Differential Equations
Editor: Vladimir
Maz’ya
Ohio State University, USA University of Liverpool, UK Link¨ oping University, SWEDEN
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Tamara Rozhkovskaya Publisher
Editor Prof. Vladimir Maz’ya Ohio State University Department of Mathematics Columbus, USA University of Liverpool Department of Mathematical Sciences Liverpool, UK Link¨ oping University Department of Mathematics Link¨ oping, Sweden
This series was founded in 2002 and is a joint publication of Springer and “Tamara Rozhkovskaya Publisher.” Each volume presents contributions from the Volume Editors and Authors exclusively invited by the Series Editor Tamara Rozhkovskaya who also prepares the Camera Ready Manuscript. This volume is distributed by “Tamara Rozhkovskaya Publisher” ([email protected]) in Russia and by Springer over all the world.
ISBN 978-0-387-85649-0 e-ISBN 978-0-387-85650-6 ISBN 978-5-901873-26-7 (Tamara Rozhkovskaya Publisher) ISSN 1571-5485 Library of Congress Control Number: 2008937494 c 2009 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, 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 o
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