Some Nonlinear Problems in Riemannian Geometry


Author: Thierry Aubin
Publisher: Springer Science & Business Media
ISBN: 3662130068
Category: Mathematics
Page: 397
View: 5409

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This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods. It explores important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved.

Polyharmonic Boundary Value Problems

Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains
Author: Filippo Gazzola,Hans-Christoph Grunau,Guido Sweers
Publisher: Springer
ISBN: 3642122450
Category: Mathematics
Page: 423
View: 2266

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This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups


Author: Wolfgang Reichel
Publisher: Springer
ISBN: 3540409157
Category: Mathematics
Page: 158
View: 2457

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A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.

Mathematical Aspects of Pattern Formation in Biological Systems


Author: Juncheng Wei,Matthias Winter
Publisher: Springer Science & Business Media
ISBN: 1447155262
Category: Mathematics
Page: 319
View: 406

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This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models. The approach adopted in the monograph is based on the following paradigms: • Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones • Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions • Extend the studies by considering extra effects or related systems, each motivated by their specific roles in developmental biology, such as spatial inhomogeneities, large reaction rates, altered boundary conditions, saturation terms, convection, many-component systems. Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.

Newsletter


Author: New Zealand Mathematical Society
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6726

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Differentialgeometrie und Minimalflächen


Author: Jost-Hinrich Eschenburg,Jürgen Jost
Publisher: Springer-Verlag
ISBN: 3642385222
Category: Mathematics
Page: 258
View: 5467

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Das vorliegende Lehrbuch bietet eine moderne Einführung in die Differenzialgeometrie - etwa im Umfang einer einsemestrigen Vorlesung. Zunächst behandelt es die Geometrie von Flächen im Raum. Viele Beispiele schulen Leser in geometrischer Anschauung, deren wichtigste Klasse die Minimalflächen bilden. Zu ihrem Studium entwickeln die Autoren analytische Methoden und lösen in diesem Zusammenhang das Plateausche Problem. Es besteht darin, eine Minimalfläche mit vorgegebener Berandung zu finden. Als Beispiel einer globalen Aussage der Differenzialgeometrie beweisen sie den Bernsteinschen Satz. Weitere Kapitel behandeln die innere Geometrie von Flächen einschließlich des Satzes von Gauss-Bonnet, und stellen die hyperbolische Geometrie ausführlich dar. Die Autoren verknüpfen geometrische Konstruktionen und analytische Methoden und folgen damit einem zentralen Trend der modernen mathematischen Forschung. Verschiedene geistesgeschichtliche Bemerkungen runden den Text ab. Die Neuauflage wurde überarbeitet und aktualisiert.

Methods in Nonlinear Analysis


Author: Kung-Ching Chang
Publisher: Springer Science & Business Media
ISBN: 3540292322
Category: Mathematics
Page: 442
View: 8803

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This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.