Local Lagrangian

A local Lagrangian of order $𝑘$ on some space $𝐹$ of smooth maps from $𝑀$ is a Lagrangian $𝐿 : 𝐹 \to Ω 𝑚 (𝑀)$ depending smoothly only on the base point $𝑥 \in 𝑀$ and partial derivatives of its argument up to order $𝑘$ . diff