Some Nonlinear Problems in Riemannian Geometry


Author: Thierry Aubin
Publisher: Springer Science & Business Media
ISBN: 3662130068
Category: Mathematics
Page: 397
View: 6365

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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.

Recent Trends in Nonlinear Partial Differential Equations

Workshop in Honor of Patrizia Pucci's 60th Birthday : Nonlinear Partial Differential Equations, May 28-June 1, 2012, University of Perugia, Perugia, Italy
Author: Patrizia Pucci
Publisher: American Mathematical Soc.
ISBN: 0821898612
Category: Mathematics
Page: 340
View: 4825

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This book is the second of two volumes that contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide ranging influence of Patrizia Pucci on the field of nonlinear analysis and partial differential equations. In her own work, Patrizia Pucci has been a seminal influence in many important areas: the maximum principle, qualitative analysis of solutions to many classes of nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain pass theorem in the critical case, critical exponents, variational identities, as well as various degenerate or singular phenomena in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume. The companion volume (Contemporary Mathematics, Volume 594) is devoted to evolution problems in nonlinear partial differential equations.

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups


Author: Wolfgang Reichel
Publisher: Springer
ISBN: 3540409157
Category: Mathematics
Page: 158
View: 1332

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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.

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: 1789

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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.

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: 1934

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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.

Differentialgeometrie und Minimalflächen


Author: Jost-Hinrich Eschenburg,Jürgen Jost
Publisher: Springer-Verlag
ISBN: 3540682937
Category: Mathematics
Page: 256
View: 1981

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Hier wird zum ersten Mal Studenten eines Anfängerkurses in Differenzialgeometrie die Theorie der Minimalflächen zugänglich gemacht. Das Buch bleibt dabei auf das Wesentliche beschränkt, ist immer gut lesbar und ausführlich motiviert. Für die Neuauflage wurde der Text in Zusammenarbeit mit J.-H. Eschenburg überarbeitet und aktualisiert. J. Jost ist seit 1993 Träger des Leibniz-Förderpreises, der an herausragende Wissenschaftler vergeben wird.

Newsletter


Author: New Zealand Mathematical Society
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2853

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Wahrscheinlichkeitstheorie und Stochastische Prozesse


Author: Michael Mürmann
Publisher: Springer-Verlag
ISBN: 364238160X
Category: Mathematics
Page: 428
View: 9121

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Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

The Ricci Flow

Techniques and Applications
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Global differential geometry
Page: N.A
View: 2314

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