On the structure of the Euler mapping

Abstract

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

7 pages