Exterior differential systems and Euler-Lagrange partial differential equations

Robert Bryant, Phillip Griffiths, Daniel Grossman

220 pages, parution le 26/09/2003

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Résumé

In Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincaré-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study. Because it plays a central role in uncovering geometric properties of differential equations, the method of equivalence is particularly emphasized. In addition, the authors discuss conformally invariant systems at length, including results on the classification and application of symmetries and conservation laws. The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws.

This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis--a subject that has been central in mathematics worldwide for the last thirty years.

Introduction
Lagrangians and Poincare-Cartan Forms
- Lagrangians and Contact Geometry
- The Euler-Lagrange System
- Noether's Theorem
- Hypersurfaces in Euclidean Space
The Geometry of Poincare-Cartan Forms
- The Equivalence Problem for n = 2
- Neo-Classical Poincare-Cartan Forms
- Digression on Affine Geometry of Hypersurfaces
- The Equivalence Problem for
- The Prescribed Mean Curvature System
Conformally Invariant Euler-Lagrange Systems
- Background Material on Conformal Geometry
- Conformally Invariant Poincare-Cartan Forms
- The Conformal Branch of the Equivalence Problem
- Conservation Laws for
- Conservation Laws for Wave Equations
Additional Topics
- The Second Variation
- Euler-Lagrange PDE Systems
- Higher-Order Conservation Laws

L'auteur - Robert Bryant

Robert Bryant is Studio Director at videogame publisher Crave Entertainment, where he has also served as QA Manager and Executive Producer of such games as World Championship Poker and Tokyo Xtreme Racer 3. He began his games career in the interactive division of Mattel, Inc., where he was lead tester on dozens of projects. He is a frequent speaker on the subjects of game testing methods and management.

L'auteur - Phillip Griffiths

Phillip Griffiths is Professor in the School of Mathematics at the Institute of Advanced Study.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	The University of Chicago Press
Auteur(s)	Robert Bryant, Phillip Griffiths, Daniel Grossman
Parution	26/09/2003
Nb. de pages	220
Format	15 x 22,7
Couverture	Broché
Poids	305g
Intérieur	Noir et Blanc
EAN13	9780226077949
ISBN13	978-0-226-07794-9