| Variational Principles for Second-Order Differential Equations, Application of the Spencer Theory of Contributor(s): Grifone, Joseph (Author), Muzsnay, Zoltan (Author) |
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ISBN: 9810237340 ISBN-13: 9789810237349 Publisher: World Scientific Publishing Company OUR PRICE: $90.25 Product Type: Hardcover Published: May 2000 |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Geometry - Analytic |
| Dewey: 515.353 |
| Physical Information: 0.76" H x 6.32" W x 8.84" (1.01 lbs) 228 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |