Aspects of the inverse problem to the calculus of variations. (English) Zbl 0674.58017

Anderson, Ian M.

Arch. Math., Brno 24, No. 4, 181-202 (1988).

This is an overview of the inverse problem of the calculus of variations associated with the variational bicomplex. The topics treated here include the local and global theories, the equivariant inverse problem and the relationship of the inverse problem to Noether’s theorem.

Reviewer: G.Toth

MSC:

58E30

Variational principles in infinite-dimensional spaces

Keywords:

Euler-Lagrange equations; Helmholtz equations; Cartan forms; Chern-Simons invariants; inverse problem; variational bicomplex; Noether’s theorem