Natural operators related with the variational calculus

Ivan Kol\'a\v r

Abstract. The basic operators of the variational calculus in
fibered manifolds are discussed from the point of view of the
theory of general natural bundles and operators. This approach
yields a clarification of the non-uniqueness phenomena related
with the higher order Poincar\'e-Cartan morphisms in the case of
several independent variables.

Keywords. Natural operator, Euler equation, Poincar\'e-Cartan morphisms.

MS Classification. 58A20, 58E30