Function Spaces, Differential Operators and Nonlinear Analysis

This volume is dedicated to our teacher and friend Hans Triebel. The core of the book 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, in honour of his 65th birthday. This was the fifth in a series of meetings organised under the same name by scientists from Finland (Helsinki, Oulu) , the Czech Republic (Prague, Plzen) and Germany (Jena) promoting the collaboration of specialists in East and West, working in these fields. This conference was a very special event because it celebrated Hans Triebel's extraordinary impact on mathematical analysis. The development of the mod­ ern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics is deeply influenced by his lasting contributions. In a series of books Hans Triebel has given systematic treatments of the theory of function spaces from different points of view, thus revealing its interdependence with interpolation theory, harmonic analysis, partial differential equations, nonlinear operators, entropy, spectral theory and, most recently, anal­ ysis on fractals. The presented collection of papers is a tribute to Hans Triebel's distinguished work. The book is subdivided into three parts: . Part I contains the two invited lectures by O.V. Besov (Moscow) and D.E. Edmunds (Sussex) having a survey character and honouring Hans Triebel's contributions.

Inhalt
Spaces of differentiable functions.- Entropy, embeddings and equations.- Nonvariational elliptic systems via Galerkin methods.- Superposition operators in Zygmund and BMO spaces.- Asymptotics of a singular solution to the Dirichlet problem for an elliptic equation with discontinuous coefficients near the boundary.- Weighted Hardy spaces on a domain and its application.- The general blow-up for nonlinear PDE's.- Laplace and Schrodinger operators on regular metric trees: the discrete spectrum case.- Inverse boundary problems in two dimensions.- On the regularity of weak solutions of elliptic systems in Banach spaces.- Complements and results on h-sets.- Lifting properties of Sobolev spaces.- Sharp estimates of approximation numbers via growth envelopes.- Sharp summability of functions from Orlicz-Sobolev spaces.- Regularity problems for some semi-linear problems.- Besov Regularity for the Neumann Problem.- Intrinsic descriptions using means of differences for Besov spaces on Lipschitz domains.- Landesman-Lazer type like results for the p-Laplacian.- On the Sobolev, Hardy and CLR inequalities associated with Schrödinger operators.- Mazur distance and normal structure in Banach spaces.- Some inequalities for integral operators, associated with the Bessel differential operator.- On determining individual behaviour from population data.- Nonlocal investigations of inhomogeneous indefinite elliptic equations via variational methods.- Regularity results and parametrices of semi-linear boundary problems of product type.- Potential estimates for large solutions of semilinear elliptic equations.- Coarea properties of Sobolev functions.- Banach envelopes of the Besov and Triebel-Lizorkin spaces and applications to PDE's.- On the flow map for a class of parabolic equations.- Spaces of functions with bounded and vanishing mean oscillation.- On equivalent quasi-norms on Lorentz spaces.- Concave functions of second order elliptic operators, kernel estimates and applications.- On approximation of solutions of parabolic functional differential equations in unbounded domains.- Function spaces in presence of symmetries: compactness of embeddings, regularity and decay of functions.- Participants FSDONA-Ol.

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