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

Demeter Krupka
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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.

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Demeter Krupka. 2002-03-18. On the local structure of the Euler-Lagrange mapping of the calculus of variations. https://arxiv.org/abs/math-ph/0203034

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