Function spaces, differential operators and nonlinear analysis

✍ Scribed by Dorothee Haroske, Thomas Runst, Hans-Jürgen Schmeisser

• Publisher: Birkhauser
• Year: 2003
• Tongue: English
• Leaves: 488
• Category: Library

✦ Synopsis

The presented collection of papers is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA-01) held in Teistungen, Thuringia/Germany, from June 28 to July 4, 2001.

They deal with the symbiotic relationship between the theory of function spaces, harmonic analysis, linear and nonlinear partial differential equations, spectral theory and inverse problems. This book is a tribute to Hans Triebel's work on the occasion of his 65th birthday. It reflects his lasting influence in the development of the modern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics. Part I contains two lectures by O.V. Besov and D.E. Edmunds having a survey character and honouring Hans Triebel's contributions. The papers in Part II concern recent developments in the field presented by D. G. de Figueiredo/C. O. Alves, G. Bourdaud, V. Maz'ya/V. Kozlov, A. Miyachi, S. Pohozaev, M. Solomyak and G. Uhlmann. Shorter communications related to the topics of the conference and Hans Triebel's research are collected in Part III

✦ Table of Contents

Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 12
Part I......Page 14
Spaces of differentiable functions......Page 16
Entropy, embeddings and equations......Page 36
Part II......Page 58
Nonvariational elliptic systems via Galerkin methods......Page 60
Superposition operators in Zygmund and BMO spaces......Page 72
Asymptotics of a singular solution to the Dirichlet problem for an elliptic equation with discontinuous coefficients near the boundary......Page 88
Weighted Hardy spaces on a domain and its application......Page 130
The general blow-up for nonlinear PDE's......Page 154
Laplace and Schrodinger operators on regular metric trees: the discrete spectrum case......Page 174
Inverse boundary problems in two dimensions......Page 196
Part III......Page 218
On the regularity of weak solutions of elliptic systems in Banach spaces......Page 220
Complements and results on h-sets......Page 232
Lifting properties of Sobolev spaces......Page 244
Sharp estimates of approximation numbers via growth envelopes......Page 250
Sharp summability of functions from Orlicz-Sobolev spaces......Page 258
Regularity problems for some semi-linear problems......Page 268
Besov Regularity for the Neumann Problem......Page 280
Intrinsic descriptions using means of differences for Besov spaces on Lipschitz domains......Page 292
Landesman-Lazer type like results for the p-Laplacian......Page 302
On the Sobolev, Hardy and CLR inequalities associated with Schrodinger operators......Page 310
Mazur distance and normal structure in Banach spaces......Page 318
Some inequalities for integral operators, associated with the Bessel differential operator......Page 330
On determining individual behaviour from population data......Page 342
Nonlocal investigations of inhomogeneous indefinite elliptic equations via variational methods......Page 354
Regularity results and parametrices of semi-linear boundary problems of product type......Page 366
Potential estimates for large solutions of semilinear elliptic equations......Page 374
Coarea properties of Sobolev functions......Page 384
Banach envelopes of the Besov and Triebel-Lizorkin spaces and applications to PDE's......Page 396
On the flow map for a class of parabolic equations......Page 406
Spaces of functions with bounded and vanishing mean oscillation......Page 416
On equivalent quasi-norms on Lorentz spaces......Page 428
Concave functions of second order elliptic operators, kernel estimates and applications......Page 440
On approximation of solutions of parabolic functional differential equations in unbounded domains......Page 452
Function spaces in presence of symmetries: compactness of embeddings, regularity and decay of functions......Page 466
Participants FSDONA-01......Page 480
Back Cover......Page 488