关于有限阶变分序列
On finite order variational sequences
摘要：
我们讨论内在方面的Krupka的方法有限阶变分序列。给出了短有限阶变分序列的商子层与适当阶jet空间上形式层的内在同构，得到了由多项式微分算子层构成的一个新的有限阶（短精确）变分序列.此外，我们提出了一个内在的制定亥姆霍兹条件的局部变异使用科拉尔介绍的技术，我们已经适应了我们的背景。最后给出了变分法反问题的最小阶解和变分平凡拉格朗日量问题的一个解。
英文摘要：
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.
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