Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

By Robert L. Bryant, P. Griffiths, D. Grossman. 2002

91 citations recorded by the source corpus.

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 Poincare-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 synthesis of partial differential equations and differential geometry should 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 30 years.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0c95b5e3f82f72878ebc829605f688d5f1cfc0a3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. D. Danielli
2. D. Nhieu
3. Nicola Garofalo
4. Robert L. Bryant
5. Manuel Ritor'e
6. Scott D. Pauls
7. L. D’Ambrosio
8. Giovanna Citti

In Numerical Analysis

1. D. Nhieu
2. D. Danielli
3. Nicola Garofalo
4. Robert L. Bryant

Citations in the corpus

• Sub-Riemannian calculus on hypersurfaces in Carnot groups (2006, methodology): “[BGG] R. Bryant, P. Griffiths & D.Grossmann, Exterior Differential Systems and Euler-Lagrange Partial Differ- ential Equations, Chicago Lec. in Mathematics, The Univ. of Chicago Press, 2003.”
• Remarks on the geometry of almost complex 6-manifolds (2005, methodology): “Because these functionals are firstorder, their Euler-Lagrange equations can be computed using the method of PoincaréCartan forms [6].”
• On some conformally invariant fully nonlinear equations, II. Liouville, Harnack and Yamabe (2005, unknown): “, [17], [26], [63], [27], [28], [23], [24], [5], [33], [35], [4], [22], [30], [29], [13], [34], [44], [45], [10], [25], [12], [31], [19] and [41].”