Some concepts of regularity for parametric multiple-integral problems in the calculus of variations
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 3, page 741-758
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topCrampin, M., and Saunders, D. J.. "Some concepts of regularity for parametric multiple-integral problems in the calculus of variations." Czechoslovak Mathematical Journal 59.3 (2009): 741-758. <http://eudml.org/doc/37955>.
@article{Crampin2009,
abstract = {We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter $(m+1)$-form are holonomic.},
author = {Crampin, M., Saunders, D. J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {parametric variational problem; regularity; multisymplectic; parametric variational problem; regularity; multisymplectic},
language = {eng},
number = {3},
pages = {741-758},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some concepts of regularity for parametric multiple-integral problems in the calculus of variations},
url = {http://eudml.org/doc/37955},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Crampin, M.
AU - Saunders, D. J.
TI - Some concepts of regularity for parametric multiple-integral problems in the calculus of variations
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 741
EP - 758
AB - We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter $(m+1)$-form are holonomic.
LA - eng
KW - parametric variational problem; regularity; multisymplectic; parametric variational problem; regularity; multisymplectic
UR - http://eudml.org/doc/37955
ER -
References
top- Cantrijn, F., Ibort, A., Léon, M. de, 10.1017/S1446788700036636, J. Australian Math. Soc. 66 (1999), 303-330. (1999) MR1694063DOI10.1017/S1446788700036636
- Cariñena, J. F., Crampin, M., Ibort, L. A., 10.1016/0926-2245(91)90013-Y, Diff. Geom. Appl. 1 (1991), 345-374. (1991) MR1244450DOI10.1016/0926-2245(91)90013-Y
- Crampin, M., Saunders, D. J., 10.1023/A:1022862117662, Acta Applicandae Math. 76 (2003), 37-55. (2003) Zbl1031.53106MR1967453DOI10.1023/A:1022862117662
- Crampin, M., Saunders, D. J., The Hilbert-Carathéodory and Poincaré-Cartan forms for higher-order multiple-integral variational problems, Houston J. Math. 30 (2004), 657-689. (2004) Zbl1057.58008MR2083869
- Crampin, M., Saunders, D. J., 10.1016/j.difgeo.2004.10.002, Diff. Geom. Appl. 22 (2005), 131-146. (2005) Zbl1073.70023MR2122738DOI10.1016/j.difgeo.2004.10.002
- Dedecker, P. M., 10.1007/BFb0087794, Lecture Notes in Mathematics, Springer 570 (1977), 395-456. (1977) Zbl0352.49018MR0458478DOI10.1007/BFb0087794
- Giaquinta, M., Hildenbrandt, S., Calculus of Variations II, Springer (1996). (1996) MR1385926
- Krupková, O., 10.1016/S0393-0440(01)00087-0, J. Geom. Phys. 43 (2002), 93-132. (2002) MR1919207DOI10.1016/S0393-0440(01)00087-0
- Rund, H., The Hamilton-Jacobi Equation in the Calculus of Variations, Van Nostrand (1966). (1966) MR0230189
- Rund, H., 10.4153/CJM-1968-062-1, Canadian J. Math. 20 (1968), 639-657. (1968) Zbl0155.44301MR0238243DOI10.4153/CJM-1968-062-1
Citations in EuDML Documents
topNotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.