Herbert Amann - Böcker

In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets.It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces.

The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations.  In particular, we are interested in such problems as:1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.

In this treatise we present the semigroup approach to quasilinear evolution equa­ of parabolic type that has been developed over the last ten years, approxi­ tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic­ ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille­ Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.

No detailed description available for "Ordinary Differential Equations".

This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the 1980s. This approach is based on the theory of nonlinear non-autonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to non-coercive quasilinear parabolic systems under nonlinear boundary conditions. This first volume is devoted to a detailed study of non-autonomous linear parabolic evolution equations in general Banach spaces. It contains an exposition of the constant domain case, leading to some improvements of the classical Sobolevski-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, the book provides systematic presentations of the theory of maximal regularity in spaces of continuous and Hoelder continuous functions, and in Lebesgue spaces. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers.Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing new results.

Der zweite Band dieser Einführung in die Analysis behandelt die Integrationstheorie von Funktionen einer Variablen, die mehrdimensionale Differentialrechnung und die Theorie der Kurven und Kurvenintegrale. Der im ersten Band begonnene moderne und klare Aufbau wird konsequent fortgesetzt. Dadurch wird ein tragfähiges Fundament geschaffen, das es erlaubt, interessante Anwendungen zu behandeln, die zum Teil weit über den in der üblichen Lehrbuchliteratur behandelten Stoff hinausgehen.Zahlreiche Übungsaufgaben von unterschiedlichem Schwierigkeitsgrad und viele informative Abbildungen runden dieses Lehrbuch ab.

This book is the first of a three volume introduction to analysis. It is distinguished by its modern and clear presentation, concentrating always on the essential concepts. In contrast to most other textbooks, there is no artificial separation between the theories of one variable and that of many variables. Emphasis is placed on the early development of a solid foundation in topology. As well, the basics of complex analysis are covered.This book is directed primarily to the students and instructors of beginning courses in analysis. But, with the many examples, exercises and the supplementary material, it is also suitable for self-study, as preparation for advanced study, and as a basis for other research in mathematics and physics."This textbook provides an outstanding introduction to analysis. It is distinguished by its high level of presentation and its focus on the essential.''Zeitschrift fur Analysis und ihre Anwendung 18, No. 4 (G. Berger, review of the first German edition)"One advantage of this presentation is that the power of the abstract concepts are convincingly demonstrated using concrete applications.''W. Grolz, review of the first German edition

As with the first, the second volume contains substantially more material than can be covered in a one-semester course. We also extend great thanks to our staff for their careful perusal of the entire manuscript and for tracking errata and inaccuracies.

This third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject.

Dieses Lehrbuch ist der erste Band einer dreiteiligen Einführung in die Analysis. Es ist durch einen modernen und klaren Aufbau geprägt, der versucht den Blick auf das Wesentliche zu richten. Anders als in den üblichen Lehrbüchern wird keine künstliche Trennung zwischen der Theorie einer Variablen und derjenigen mehrerer Veränderlicher vorgenommen. Der Leser soll in dem Erkennen der wesentlichen Inhalte und Ideen der Analysis geschult werden und sich ein solides Fundament für das Studium tieferliegender Theorien erwerben. Das Werk richtet sich an Hörer und Dozenten der Anfängervorlesung der Analysis. Durch zahlreiche Beispiele, Übungsaufgaben und Ergänzungen zum üblichen Vorlesungsstoff ist der Text ausserdem zum Selbststudium, als Vorlage für vertiefende Seminare und als Grundlage für das gesamte Mathematik- bzw. Physikstudium geeignet.

Günter Lumer was an outstanding mathematician whose work has great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips of 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of Günter Lumer.