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The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.

Differential equations, Partial. --- Differential equations, Elliptic. --- Differential equations, Parabolic. --- Bifurcation theory. --- Fluid mechanics. --- Hydromechanics --- Continuum mechanics --- Differential equations, Nonlinear --- Stability --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Partial differential equations --- Numerical solutions --- Global analysis (Mathematics). --- Differential equations, partial. --- Potential theory (Mathematics). --- Numerical analysis. --- Mathematical optimization. --- Analysis. --- Partial Differential Equations. --- Potential Theory. --- Numerical Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Fluid- and Aerodynamics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mechanics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Calculus of variations. --- Fluids. --- Hydraulics --- Physics --- Hydrostatics --- Permeability --- Isoperimetrical problems --- Variations, Calculus of --- 517.1 Mathematical analysis

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This third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject. As with the ?rst two, this volume contains more material than can treated in a single course. It is therefore important in preparing lectures to choose a suitable subset of its content; the remainder can be treated in seminars or left to independent study. For a quick overview of this content, consult the table of contents and the chapter introductions. Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope that its numerous glimpses into more advanced analysis will arouse curiosity and so invite students to further explore the beauty and scope of this branch of mathematics. In writing this volume, we counted on the invaluable help of friends, c- leagues, sta?, and students. Special thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker, who worked through the entire text cr- ically and so helped us remove errors and make substantial improvements. Our thanks also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read the majority of the manuscript and pointed out various inconsistencies. Without the inestimable e?ortofour “typesetting perfectionist”, this volume could not have reached its present form: her tirelessness and patience with T X E and other software brought not only the end product, but also numerous previous versions,to a high degree of perfection. For this contribution, she has our greatest thanks.

Electronic books. -- local. --- Mathematical analysis. --- Mathematics. --- Mathematical analysis --- Applied Mathematics --- Engineering & Applied Sciences --- Math --- 517.1 Mathematical analysis --- Analysis (Mathematics). --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Measure theory. --- Analysis. --- Measure and Integration. --- Global Analysis and Analysis on Manifolds. --- Science --- Global analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Geometry, Differential --- Topology --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)

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Functional analysis --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde

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Der dritte und letzte Band dieser Reihe ist der Integrationstheorie und den Grundlagen der globalen Analysis gewidmet. Es wird wiederum viel Wert auf einen modernen und klaren Aufbau gelegt, der nicht nur eine wohl strukturierte schöne Theorie liefert, sondern dem Leser auch schlagkräftige Werkzeuge für seine weitere Beschäftigung mit der Mathematik in die Hand gibt. Aus diesem Grund wird beispielsweise konsequent das Bochner-Lebesguesche Integral entwickelt, welches ein unverzichtbares Hilfsmittel für die moderne Theorie der partiellen Differentialgleichungen darstellt. Ebenso wird eine Version des Stokesschen Satzes bewiesen, welche den praktischen Bedürfnissen der Mathematik und theoretischen Physik weitgehend Rechnung trägt. Wie bereits in den früheren Bänden, werden auch hier zahlreiche Ausblicke auf weiterführende Theorien gegeben, die dem Leser einen Eindruck von der Bedeutung und der Stärke der entwickelten Theorien vermitteln sollen. Daneben dienen diese Abschnitte dazu, den bereitgestellten Stoff weiter einzuüben und zu vertiefen. Zahlreiche Beispiele, konkrete Rechnungen, eine Vielzahl von Übungsaufgaben und viele Abbildungen machen dieses Lehrbuch zu einem verlässlichen Begleiter durch das gesamte Studium.

Mathematical analysis. --- Analysis (Mathematics). --- Measure theory. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Analysis. --- Measure and Integration. --- Global Analysis and Analysis on Manifolds.

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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.

Mathematical analysis. --- Analysis (Mathematics). --- Analysis.