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Variational Principles For Second-order Differential Equations, Application Of The Spencer Theory Of
eBook
ISBN/EAN: 9789814495363
Umbreit-Nr.: 9574244
Sprache:
Englisch
Umfang: 228 S.
Format in cm:
Einband:
Keine Angabe
Erschienen am 25.05.2000
Auflage: 1/2000
E-Book
Format: PDF
DRM: Adobe DRM
- Kurztext
- 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.