On the geometry of variational calculus on some functional bundles. (English) Zbl 1195.58007

Janyška, Josef; Cabras, Antonella; Kolář, Ivan

Note Mat. 26, No. 2, 51-67 (2006).

Summary: We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms between our bundles of smooth maps, we introduce the concept of fiberwise \((k,r)\)-jet. The relations to the Euler-Lagrange morphism of the variational calculus are described.

MSC:

58E30	Variational principles in infinite-dimensional spaces
49Q20	Variational problems in a geometric measure-theoretic setting

Keywords:

formal exterior differential; bundle of smooth maps; operator order of a morphism; fiberwise \((k,r)\)-jet; Euler-Lagrange morphism