A global version of the inverse problem of the calculus of variations
The author solves a global version of the inverse problem in the calculus of variations. The essential task in this problem is to determine under what conditions, if any, given field equations are the Euler-Lagrange equations corresponding to a Lagrangian. Unfortunately for the author, a more complete and elegant solution was given earlier by \textit{A. M. Vinogradov} [Sov. Math., Dokl. 18(1977), 1200--1204 (1978); translation from Dokl. Akad. Nauk SSSR 236, 284--287 (1977; Zbl 0403.58005), Sov.. Math., Dokl. 19, 144--148 (1978); translation from Dokl. Akad. Nauk SSSR 238, 1028--1031 (1978; Zbl 0406.58015)].
global version of the inverse problem in the calculus of variations
Euler-Lagrange equations corresponding to a Lagrangian
scientific article; zbMATH DE number 3725348