Existe-t-il, en calcul des variations, un formalisme de Hamilton-Jacobi- E. Cartan pour les intégrales multiples d’ordre supérieur ? (Does there exist a formalism of Hamilton-Jacobi-E. Cartan for higher-order multiple integrals in the calculus of variations ?). (French) Zbl 0577.49028

In a recent article M. Francaviglia and D. Krupka [Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 37, 295-315 (1982; Zbl 0516.70022)] announced a Hamiltonian formalism in higher order variational problems. The author shows by a counter-example that Theorem 2 in the paper loc. cit. is wrong and suggests a way to discover a positive solution to the problem of the Hamilton-Jacobi-E. Cartan formalism for higher order multiple integrals in the calculus of variations.
Reviewer: C.Udrişte


49Q99 Manifolds and measure-geometric topics
58A15 Exterior differential systems (Cartan theory)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70H20 Hamilton-Jacobi equations in mechanics


Zbl 0516.70022