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VARIATIONAL PRINCIPLES FOR SECOND-ORDER DIFFERENTIAL EQUATIONS, APPLICATION OF THE SPENCER THEORY OF
Author(s): Joseph Grifone (Author), Zoltan Muzsnay (Author)
- Publisher: World Scientific Publishing Company
- Publication Date: May 26, 2000
- Language: English
- Print length: 228 pages
- ISBN-10: 9810237340
- ISBN-13: 9789810237349
Book Description
The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.
Editorial Reviews
Review
Everybody seriously interested in the modern theory of the inverse problem of the calculus of variations should read this. — Zentralblatt MATH
