Wow! eBook
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 Co Pte Ltd
- Publication Date: 26 May 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.
