Function Spaces, Differential Operators and Nonlinear Analysis: The Hans Triebel Anniversary Volume

488 Pages·2003·8.15 MB·English

by  Dorothee Haroske

Function
Differential Oper
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Dorothee Haroske
Thomas Runst
Hans-Jurgen Schmeisser
Editors
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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: [e-mail]
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
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ISBN 3-7643-6935-3
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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