标题： 关于有限阶变分序列 显示英文标题

标题： On finite order variational sequences

摘要： 我们讨论Krupka关于有限阶变分序列的内在方面。 我们给出了短有限阶变分序列的商子层与适当阶数的喷射空间上的形式层的内在同构，得到一个新的有限阶（短正合）变分序列，该序列由多项式微分算子层构成。 此外，我们使用Kolar引入的一种技术，对该技术进行了适应，以获得局部变分性的Helmholtz条件的内在表述。 最后，我们提供了变分法逆问题的最小阶解，以及变分平凡拉格朗日量的问题的解。 显示英文摘要

摘要： We discuss intrinsic aspects of Krupka's approach to finite-order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite-order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite-order (short exact) variational sequence which is made by sheaves of polynomial differential operators. Moreover, we present an intrinsic formulation for the Helmholtz condition of local variationality using a technique introduced by Kolar that we have adapted to our context. Finally, we provide the minimal order solution to the inverse problem of the calculus of variations and a solution of the problem of the variationally trivial Lagrangian.