On the structure of the Euler mapping

Abstract

The goal of this paper is to give acomplete description of the Lagrange functions L satisfying $\cal E (L)=0$. In other words we shall study the kernel of the linear mapping $\cal L (J^1) \ni L \to \cal E (L) \in \Omega^1(J^2)$, which will be referred to as the Euler mapping.