Bøger af Hans Triebel

The present Teubner-Text contains the contributions from the International Workshop "Analysis in Domains and on Manifolds with Singularities", Breitenbrunn, Germany, 30. April-5. May 1990. In recent years the analysis on manifolds with singularities became more and more interesting, not only because of the progress in solving corresponding singular problems in partial differential equations but also of the new relations to other parts of mathematics such as geometry, topology and mathematical physics. Other motivations come from concrete models in engineering and applied sciences which lead to partial differential equations in domains with a piece-wise smooth geometry (conical points, edges, comers, ... , higher singularities), piece-wise smooth data or boundary and transmission conditions, degenerate coefficients, and so on. There are natural relations to the numerical analysis where also the asymptotics of solutions close to the singularities playa role. As for the smooth cases it is necessary to develop structure principles and unified theories that cover as much as possible the huge variety of concrete situations, often being treated by individual papers under very specific assumptions.

Keine ausführliche Beschreibung für "Analysis und mathematische Physik" verfügbar.

This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations. The book is self-contained, although some parts may be considered as a continuation of the author's book "Fractals and Spectra" (MMA 91). It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated.

The present Teubner-Text contains invited surveys and shorter communications con­ nected with the International Conference "Function Spaces, Differential Operators and Non­ linear Analysis", which took place in Friedrichroda (Thuringia, Germany) from September 20-26, 1992. The main subjects are weil reflected by the table of contents. 55 mathematicians attended the conference, many of them from eastern countries. We take the opportunity to thank DFG for financial support, which enabled us to invite mathematicians from the former socialist countries, and especially from the former Soviet Union, and which gave us the pos­ sibility to maintain and to strengthen our contacts to these centers of the theory of function spaces and its application to PDE's, \li'DE's and approximation theory. The organization of the conference as weil as the final preparation of this text was mostly done by our co-workers in Jena. We wish to thank all of them for the generaus support they gave us far beyond their duties (whatever this means in connection with the organization of a conference). The final preparation of this text was mainly done by Dr. M. Malarski. Fur­ thermore Dr. M. Geisler, Ms. D. Haroske and Dr. W. Sicke! converted some manuscript in readable papers on TEX-standard Ievel. We wish to thank them for doing this time-consuming work. Jena, May 13, 1993 H.-J. Schmeisser H. Triebe! Contents Survey Articles 9 I Herbert Amann Nonhomogeneaus Linear and Quasilinear Elliptic and Parabolic Boundary Value Pr- lems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Gerard Bourdaud The Functional Calculus in Sobolev Spaces . . . . . . . . . . . . . . . . . . . 127 . . . . .

This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".

Deals with the theory of function spaces of type Bspq and Fspq. This book analyzes the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds.

The distribution of the eigenvalues of differential operators has long fascinated mathematicians. Advances have shed light upon classical problems in this area, and this book presents a fresh approach, largely based upon the results of the authors. The treatment is largely self-contained and accessible to non-specialists. Both experts and newcomers alike will welcome this unique exposition.

This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations. The book is self-contained, although some parts may be considered as a continuation of the author's book Fractals and Spectra. It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated. - - - The book under review can be regarded as a continuation of [his book on "e;Fractals and spectra"e;, 1997] (...) There are many sections named: comments, preparations, motivations, discussions and so on. These parts of the book seem to be very interesting and valuable. They help the reader to deal with the main course. (Mathematical Reviews)

n This book deals with several aspects of fractal geometry in ? which are closely connected with Fourier analysis, function spaces, and appropriate (pseudo)differ- tial operators. It emerged quite recently that some modern techniques in the theory of function spaces are intimately related to methods in fractal geometry. Special attention is paid to spectral properties of fractal (pseudo)differential operators; in particular we shall play the drum with a fractal layer. In some sense this book may be considered as the fractal twin of [ET96], where we developed adequate methods to handle spectral problems of degenerate n pseudodifferential operators in ? and in bounded domains. Besides a few special properties of function spaces we relied there on sharp estimates of entropy numbers of compact embeddings between these spaces and their relations to the distribution of eigenvalues. Some of the main assertions of the present book are based on just these techniques but now in a fractal setting. Since virtually nothing of these new methods is available in literature, a substantial part of what we have to say deals with recent developments in the theory of function spaces, also for their own sake. In this respect the book might also be considered as a continuation of [Tri83] and [Tri92].

This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis.

The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where -