On the equivalence of variational problems. I. (English) Zbl 0764.49008

Summary: We deal with the absolute equivalence of one-dimensional variational problems. The term “absolute” means that the underlying space is not given in advance: the transformations may be quite general and need not preserve the order of derivatives. Then the use of jets of infinite order is advisable and an appropriately modified E. Cartan’s moving frame method proves to be very effective.


49J40 Variational inequalities
Full Text: DOI


[1] Cartan, E, Sur un problème d’équivalence et la théorie des espaces métriques généralisés, (), 1131-1153, Paris · JFM 56.1193.02
[2] Cartan, E, La géométrie de l’intégrale ∝ F(x, y, y′, y″)dx, (), 1341-1368, Paris · JFM 62.0873.02
[3] Chrastina, J, What the differential equations should be, (), 42-50 · Zbl 0571.58030
[4] Chrastina, J, Formal calculus of variations on fibered manifolds, (), Brno, Czechoslovakia · Zbl 0696.49075
[5] Griffiths, P.A, Exterior differential systems and the calculus of variations, () · Zbl 0178.23803
[6] Hsu, L; Kamran, N; Olver, P.J, Equivalence for higher order Lagrangians, II, J. math. phys., 30, 902-906, (1989)
[7] Kamran, N; Olver, P.J, Equivalence problems for first order Lagrangians on the line, J. differential equations, 80, 32-78, (1989) · Zbl 0677.49034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.