Nonlinear Partial Differential Equations in Geometry and Physics: The 1995 Barrett Lectures: v. 29 (Progress in Nonlinear Differential Equations and Their Applications) - Hardcover

Hardcover

ISBN 10: 3764354933 ISBN 13: 9783764354930

Verlag: Birkhäuser, 1997

Inhaltsangabe

New Directions in 4-Manifold Theory.- Lecture 1: Donaldson and Seiberg-Witten Invariants.- Lecture 2: The Immersed Thorn Conjecture.- Lecture 3: Intersection Forms of Smooth 4-Manifolds.- References.- On the Regularity of Classical Field Theories in Minkowski Space-Time E3+1.- 1 Relativistic Field Theories.- 2 The Problem of Break-down.- 3 Energy estimates and the Problem of Optimal Local Well Posedness.- 4 Proof of the Null Estimates.- 5 The Proof of Theorem 4.- 6 Conclusions.- Static and Moving Vortices in Ginzburg-Landau Theories.- Lecture 1.- 1 Background and Models.- 2 The Work of Bethuel-Brézis-Hélein and Others.- 3 Some Generalizations.- Lecture 2.- 1 Renormalized Energy.- 2 A Technical Result.- 3 Proof of Theorem A.- 4 Proof of Theorem B.- Lecture 3: The Dynamical Law of Ginzburg-Landau Vortices.- 1 Gor'kov-Eliashberg's Equation.- 2 Uniqueness of Asymptotic Limit.- 3 Vortex Motion Equations.- References.- Wave Maps.- 1 Local existence. Energy method.- 1.1 The setting.- 1.2 Wave Maps.- 1.3 Examples.- 1.4 Basic questions.- 1.5 Energy estimates.- 1.6 L2-theory.- 1.7 Local existence for smooth data.- 1.8 A slight improvement.- 1.9 Global existence, the case m = 1.- 2 Blow-up and non-uniqueness.- 2.1 Overview.- 2.2 Regularity in the elliptic and parabolic cases.- 2.3 Regularity in the hyperbolic case.- 3 The conformai case m = 2.- 3.1 Overview.- 3.2 The equivariant case.- 3.3 Towards well-posedness for general targets.- 3.4 Approximation solutions.- 3.5 Convergence.- References.

Über diesen Titel

Críticas

"All the essays are on the topmost professional level and are highly recommended to researchers and especially to young specialists in mathematical physics, PDE, differential geometry and topology, because they illustrate brilliantly the recent tendency in the theory of nonlinear PDEa ]namely the realization that structures originally introduced in the context of mathematical models in theoretical physics may turn out to have important applications in topology and (differential) geometry." --Mathematica Bohemica

Reseña del editor

The subject of nonlinear partial differential equations is experiencing a period of intense activity in the study of systems underlying basic theories in geometry, topology and physics. These mathematical models share the property of being derived from variational principles. Understanding the structure of critical configurations and the dynamics of the corresponding evolution problems is of fundamental importance for the development of the physical theories and their applications. This volume contains survey lectures in four different areas, delivered by leading resarchers at the 1995 Barrett Lectures held at The University of Tennessee: nonlinear hyperbolic systems arising in field theory and relativity (S. Klainerman); harmonic maps from Minkowski spacetime (M. Struwe); dynamics of vortices in the Ginzburg-Landau model of superconductivity (F.-H. Lin); the Seiberg-Witten equations and their application to problems in four-dimensional topology (R. Fintushel). Most of this material has not previously been available in survey form. These lectures provide an up-to-date overview and an introduction to the research literature in each of these areas, which should prove useful to researchers and graduate students in mathematical physics, partial differential equations, differential geometry and topology.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 1997
• ISBN 10: 3764354933
• ISBN 13: 9783764354930
• Einband: Tapa dura
• Sprache: Englisch
• Anzahl der Seiten: 172
• Herausgeber: Baker Garth, Freire Alexandre
• Kontakt zum Hersteller: Nicht verfügbar