Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

by Robert Bryant, Phillip Griffiths, Daniel Grossman
     
 

ISBN-10: 0226077934

ISBN-13: 9780226077932

Pub. Date: 07/28/2003

Publisher: University of Chicago Press

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

…  See more details below

Overview

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.

Read More

Product Details

ISBN-13:
9780226077932
Publisher:
University of Chicago Press
Publication date:
07/28/2003
Series:
Chicago Lectures in Mathematics Series
Edition description:
1
Pages:
216
Product dimensions:
6.20(w) x 9.20(h) x 0.70(d)

Table of Contents

Preface
Introduction
1Lagrangians and Poincare-Cartan Forms9
1.1Lagrangians and Contact Geometry9
1.2The Euler-Lagrange System15
1.3Noether's Theorem22
1.4Hypersurfaces in Euclidean Space29
2The Geometry of Poincare-Cartan Forms45
2.1The Equivalence Problem for n = 247
2.2Neo-Classical Poincare-Cartan Forms60
2.3Digression on Affine Geometry of Hypersurfaces66
2.4The Equivalence Problem for [actual symbol not reproducible] 373
2.5The Prescribed Mean Curvature System82
3Conformally Invariant Euler-Lagrange Systems87
3.1Background Material on Conformal Geometry88
3.2Conformally Invariant Poincare-Cartan Forms105
3.3The Conformal Branch of the Equivalence Problem110
3.4Conservation Laws for [Delta]u = Cu [actual symbol not reproducible]118
3.5Conservation Laws for Wave Equations126
4Additional Topics141
4.1The Second Variation141
4.2Euler-Lagrange PDE Systems158
4.3Higher-Order Conservation Laws176

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >