On the local structure of the Euler-Lagrange mapping of the calculus of variations

Abstract

The purpose of this paper is to announce some new results on the structure of the higher order Euler-Lagrange mapping of the multiple-integral variational calculus on fibered manifolds,namely a description of its kernel and its image,and an explicit characterization of the conditions under which a system of partial differential equations (of arbitrary order)is a system of the Euler--Lagrange equations.

arXiv comment6 pages

References in corpus (1)

• Some geometric aspects of variational problems in fibred manifolds

Cited by in corpus (4)

• Canonical variational completion of differential equations
• On the extraction of the boundary conditions and the boundary ports in second-order field theories
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• Cohomology groups for Lagrange complexes that are invariant under a pseudogroup of local transformations