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A global version of the inverse problem of the calculus of variations. (English) Zbl 0463.58015
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 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)].
Reviewer: C. S. Sharma

MSC:
58E30 Variational principles in infinite-dimensional spaces
49N45 Inverse problems in optimal control
70H03 Lagrange’s equations
58A20 Jets in global analysis
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
57R25 Vector fields, frame fields in differential topology
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