On the equivalence of variational problems. II. (English) Zbl 0821.49009

Chrastina, Jan

Arch. Math., Brno 29, No. 3-4, 197-220 (1993).

The paper follows a previous one by the same author on the equivalence of two variational problems with differential constraints [J. Differ. Equations 98, No. 1, 76-90 (1992; Zbl 0764.49008)]. More precisely, it deals with problems of the type: to find the optimal solutions of an integral functional \[ \int f \bigl( x,y(x), y_ 1(x), \dots, y_ n(x) \bigr) dx \quad y^ i_ s = d^ s y^ i/d x^ s,\;i = 1, \dots, m,\;s \in \mathbb{N}, \] subjected to constraints of the type \[ \partial^ k g^ i = 0,\;j = 1, \dots, c,\;k = 0,1, \dots \quad \partial = \partial/ \partial x + \sum y^ i_{k + 1} \partial/ \partial y^ i_ s. \] The technique he adopts is an infinite dimensional variant of Cartan’s moving frame method.

Reviewer: A.Salvadori (Perugia)

MSC:

49J40	Variational inequalities
49L99	Hamilton-Jacobi theories
58A17	Pfaffian systems

Keywords:

Poincaré-Cartan form; variational problem with differential constraints; integral functional; Cartan’s moving frame method

Citations:

Zbl 0764.49008