Function Spaces, Differential Operators and Nonlinear Analysis: The Hans Triebel Anniversary Volume PDF
Preview Function Spaces, Differential Operators and Nonlinear Analysis: The Hans Triebel Anniversary Volume
Function Differential Oper [('P'f) () I 2'sq I I LP (Rn) Dorothee Haroske Thomas Runst Hans-Jurgen Schmeisser Editors ,If; Function Spaces, Differential Operators and Nonlinear Analysis The Hans Triebel Anniversary Volume Dorothee Haroske Thomas Runst Hans-Jurgen Schmeisser Editors Birkhauser Verlag Basel Boston - Berlin Editors' address: Institute of Mathematics Friedrich-Schiller-University 07740 Jena Germany e-mail: [email protected] 2000 Mathematics Subject Classification 35-02, 42-02, 46-02, 46E35, 47-02 A CIP catalogue record for this book is available from the library of Congress, Washington D.C., USA Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Blbliothek lists this publication in the Deutsche Nationalbibliograhe; detailed bibliographic data is availa- ble in the Internet at <http://dnb.ddb.de>. ISBN 3-7643-6935-3 Birkhauser Verlag, Basel - Boston - Berlin This work is subject to copyright. NI 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 micro- films or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. ® 2003 Birkhtuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland Member of the BertelsmannSpnnger Publishing Group Printed on acid-free paper produced from chlorine-free pulp. TCF Cover design: Micha Lotrovsky, CH-4106 Therwil, Switzerland Printed in Germany ISBN 3-7643-6935-3 987654321 www.birkhauser.ch This collection of research papers is dedicated to Hans Triebel on the occasion of his 65th birthday Contents Preface ................................................................... xi Part I .................................................................... 1 Oleg Besov and Gennadiy Kalyabin Spaces of differentiable functions ..................................... 3 David E. Edmunds Entropy, embeddings and equations .................................. 23 Part II ................................................................... 45 Claudianor O. Alves and Djairo G. de Figueiredo Nonvariational elliptic systems via Galerkin methods ................. 47 G46rard Bourdaud Superposition operators in Zygmund and BMO spaces ............... 59 Vladimir Kozlov and Vladimir Maz'ya Asymptotics of a singular solution to the Dirichlet problem for an elliptic equation with discontinuous coefficients near the boundary ................................................... 75 Akihiko Miyachi Weighted Hardy spaces on a domain and its application .............. 117 Stanislav Pohozaev The general blow-up for nonlinear PDE's ............................ 141 Michael Solomyak Laplace and Schrodinger operators on regular metric trees: the discrete spectrum case ........................................... 161 Gunther Uhlmann Inverse boundary problems in two dimensions ........................ 183 Part III .................................................................. 205 Marina Borovikova and Riidiger Landes On the regularity of weak solutions of elliptic systems in Banach spaces ................................................... 207 viii Contents Michele Bricchi Complements and results on h-sets .................................. 219 Viktor I. Burenkov Lifting properties of Sobolev spaces .................................. 231 Ant6nio M. Caetano and Dorothee D. Haroske Sharp estimates of approximation numbers via growth envelopes .................................................... 237 Andrea Cianchi Sharp summability of functions from Orlicz-Sobolev spaces ........... 245 Serguei Dachkovski .................. Regularity problems for some semi-linear problems 255 Stephan Dahlke Besov Regularity for the Neumann Problem ......................... 267 Sophie Dispa Intrinsic descriptions using means of differences for Besov spaces on Lipschitz domains ................................... 279 Pavel Drdbek Landesman-Lazer type like results for the p-Laplacian ................ 289 W.D. Evans On the Sobolev, Hardy and CLR inequalities associated with Schrodinger operators .......................................... 297 Ji Gao .............. Mazur distance and normal structure in Banach spaces 305 Vagif S. Guliev Some inequalities for integral operators, associated with the Bessel differential operator ....................................... 317 Mats Gyllenberg, Andrei Osipov, and Lassi Paivarinta .......... On determining individual behaviour from population data 329 Yavdat Il'yasov and Thomas Runst Nonlocal investigations of inhomogeneous indefinite ............................ elliptic equations via variational methods 341 Jon Johnsen Regularity results and parametrices of semi-linear .................................. boundary problems of product type 353 Denis A. Labutin Potential estimates for large solutions of semilinear elliptic equations .................................................... 361 Contents ix Jan Maly Coarea properties of Sobolev functions ............................... 371 Osvaldo Mendez and Marius Mitrea Banach envelopes of the Besov and Triebel-Lizorkin spaces and applications to PDE's ........................................... 383 Luc Molinet, Francis Ribaud, and Abdellah Youssfi On the flow map for a class of parabolic equations ................... 393 David Opela Spaces of functions with bounded and vanishing mean oscillation ..................................................... 403 Bohumir Opic On equivalent quasi-norms on Lorentz spaces ........................ 415 Evgeniy Pustylnik Concave functions of second order elliptic operators, kernel estimates and applications .................................... 427 Laszlo Simon On approximation of solutions of parabolic functional differential equations in unbounded domains ......................... 439 Leszek Skrzypczak Function spaces in presence of symmetries: compactness of embeddings, regularity and decay of functions ....................... 453 Participants FSDONA-01 ................................................. 467
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