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Title: Examples from the calculus of variations. IV. Concluding review (English)
Author: Chrastina, Jan
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 126
Issue: 4
Year: 2001
Pages: 691-710
Summary lang: English
Category: math
Summary: Variational integrals containing several functions of one independent variable subjected moreover to an underdetermined system of ordinary differential equations (the Lagrange problem) are investigated within a survey of examples. More systematical discussion of two crucial examples from Part I with help of the methods of Parts II and III is performed not excluding certain instructive subcases to manifest the significant role of generalized Poincaré-Cartan forms without undetermined multipliers. The classical Weierstrass-Hilbert theory is simulated to obtain sufficient extremality conditions. Unlike the previous parts, this article is adapted to the category of continuous objects and mappings without any substantial references to the general principles, which makes the exposition self-contained. (English)
Keyword: Lagrange problem
Keyword: Poincaré-Cartan form
Keyword: Hamiltonian-Jacobi equation
Keyword: Weierstrass-Hilbert method
MSC: 49-01
MSC: 49-02
MSC: 49K27
MSC: 49K45
MSC: 58E30
idZBL: Zbl 1008.49015
idMR: MR1869462
DOI: 10.21136/MB.2001.134113
Date available: 2009-09-24T21:56:05Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] J. Chrastina: Examples from the calculus of variations I. Nondegenerate problems.Math. Bohem. 125 (2000), 55–76. Zbl 0968.49001, MR 1752079
Reference: [2] V. Chrastinová, V. Tryhuk: The Mayer problem.(to appear).
Reference: [3] V. Tryhuk: On a degenerate variational problem.(to appear).


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