About: On regularization of variational problems in first-order field theory

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Standard Hamiltonian formulation of field theory is founded upon the Poicaré-Cartan form. Accordingly, a first-order Lagrangian L is called regular if $\det ({{\pr^2 L} \over {\pr y^\sigma_i \pr y^\nu_j}}) \ne 0$; in this case the Hamilton equations are equivalent with the Euler-Lagrange equations. Keeping the requirement on equivalence of the Hamilton and Euler-Lagrange equations as a (geometric) definition of regularity, and considering more general Lepagean equivalents of a Lagrangian than the Poincaré-Cartan equivalent, we obtain a regularity condition, depending not only on a Lagrangian but also on 2-contact parts of its Lepagean equivalents. Standard Hamiltonian formulation of field theory is founded upon the Poicaré-Cartan form. Accordingly, a first-order Lagrangian L is called regular if $\det ({{\pr^2 L} \over {\pr y^\sigma_i \pr y^\nu_j}}) \ne 0$; in this case the Hamilton equations are equivalent with the Euler-Lagrange equations. Keeping the requirement on equivalence of the Hamilton and Euler-Lagrange equations as a (geometric) definition of regularity, and considering more general Lepagean equivalents of a Lagrangian than the Poincaré-Cartan equivalent, we obtain a regularity condition, depending not only on a Lagrangian but also on 2-contact parts of its Lepagean equivalents. (en)
Title	On regularization of variational problems in first-order field theory On regularization of variational problems in first-order field theory (en)
skos:prefLabel	On regularization of variational problems in first-order field theory On regularization of variational problems in first-order field theory (en)
skos:notation	RIV/47813059:19610/01:00000059!RIV/2002/MSM/196102/N
http://linked.open.../vavai/riv/strany	133;140
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM 192400002)
http://linked.open...iv/cisloPeriodika	66
http://linked.open...vai/riv/dodaniDat	2002
http://linked.open...aciTvurceVysledku	Krupková, Olga
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	689928
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/01:00000059
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Lagrangian; Poincaré-Cartan form; Lepage form; Hamilton extremals; Hamilton equations; regularity (en)
http://linked.open.../riv/klicoveSlovo	Lagrangian Poincaré-Cartan form regularity Lepage form Hamilton equations Hamilton extremals
http://linked.open...odStatuVydavatele	IT - Italská republika
http://linked.open...ontrolniKodProRIV	[09E1F95D57DA]
http://linked.open...i/riv/nazevZdroje	Rendiconti Circcolo Matematico di Palermo, Serie II Supplemento
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...ocetUcastnikuAkce	0 (xsd:int)
http://linked.open...nichUcastnikuAkce	0 (xsd:int)
http://linked.open...UplatneniVysledku	2001
http://linked.open...v/svazekPeriodika	2001
http://linked.open...iv/tvurceVysledku	Krupková, Olga Smetanová, Dana
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20192400002
issn	0009-725X
number of pages	8 (xsd:int)
http://localhost/t...ganizacniJednotka	19610

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