Second variational derivative of local variational problems and conservation laws

Marcella Palese; Ekkehart Winterroth; E. Garrone

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 5, page 395-403
  • ISSN: 0044-8753

Abstract

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We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that the corresponding local system of Euler–Lagrange forms is variationally equivalent to a global one.

How to cite

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Palese, Marcella, Winterroth, Ekkehart, and Garrone, E.. "Second variational derivative of local variational problems and conservation laws." Archivum Mathematicum 047.5 (2011): 395-403. <http://eudml.org/doc/246837>.

@article{Palese2011,
abstract = {We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that the corresponding local system of Euler–Lagrange forms is variationally equivalent to a global one.},
author = {Palese, Marcella, Winterroth, Ekkehart, Garrone, E.},
journal = {Archivum Mathematicum},
keywords = {fibered manifold; jet space; Lagrangian formalism; variational sequence; second variational derivative; cohomology; symmetry; conservation law; fibered manifold; jet space; Lagrangian formalism; variational sequence; second variational derivative; cohomology; symmetry; conservation law},
language = {eng},
number = {5},
pages = {395-403},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Second variational derivative of local variational problems and conservation laws},
url = {http://eudml.org/doc/246837},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Palese, Marcella
AU - Winterroth, Ekkehart
AU - Garrone, E.
TI - Second variational derivative of local variational problems and conservation laws
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 5
SP - 395
EP - 403
AB - We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that the corresponding local system of Euler–Lagrange forms is variationally equivalent to a global one.
LA - eng
KW - fibered manifold; jet space; Lagrangian formalism; variational sequence; second variational derivative; cohomology; symmetry; conservation law; fibered manifold; jet space; Lagrangian formalism; variational sequence; second variational derivative; cohomology; symmetry; conservation law
UR - http://eudml.org/doc/246837
ER -

References

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