Examples from the calculus of variations. IV. Concluding review

Chrastina, Jan. "Examples from the calculus of variations. IV. Concluding review." Mathematica Bohemica 126.4 (2001): 691-710. <http://eudml.org/doc/248868>.

@article{Chrastina2001,
abstract = {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.},
author = {Chrastina, Jan},
journal = {Mathematica Bohemica},
keywords = {Lagrange problem; Poincaré-Cartan form; Hamiltonian-Jacobi equation; Weierstrass-Hilbert method; Lagrange problem; Poincaré-Cartan form; Hamilton-Jacobi equation; Weierstrass-Hilbert method},
language = {eng},
number = {4},
pages = {691-710},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Examples from the calculus of variations. IV. Concluding review},
url = {http://eudml.org/doc/248868},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Chrastina, Jan
TI - Examples from the calculus of variations. IV. Concluding review
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 4
SP - 691
EP - 710
AB - 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.
LA - eng
KW - Lagrange problem; Poincaré-Cartan form; Hamiltonian-Jacobi equation; Weierstrass-Hilbert method; Lagrange problem; Poincaré-Cartan form; Hamilton-Jacobi equation; Weierstrass-Hilbert method
UR - http://eudml.org/doc/248868
ER -