Publication detail

On the Lagrange variational problem

CHRASTINOVÁ, V. TRYHUK, V.

Original Title

On the Lagrange variational problem

Type

journal article in Web of Science

Language

English

Original Abstract

We investigate the stationarity of variational integrals evaluated on solutions of a system of differential equations. First, the fundamental concepts are relieved of accidental structures and of hypothetical assumptions. The differential constraints, stationarity and the Euler-Lagrange equations related to Poincare-Cartan forms do not require any reference to coordinates or deep existence theorems for boundary value problems. Then, by using the jet formalism, the Lagrange multiplier rule is proved for all higher-order variational integrals and arbitrary compatible systems of differential equations. The self-contained exposition is based on the standard theory of differential forms and vector fields.

Keywords

Lagrange variational problem; Lagrange multipliers; diffiety; Poincar?-Cartan form

Authors

CHRASTINOVÁ, V.; TRYHUK, V.

Released

15. 6. 2023

Publisher

Polish Academy of Sciences, Institute of Mathematics

Location

Warszawa

ISBN

0066-2216

Periodical

Annales Polon.Math.

Year of study

130

Number

2

State

Republic of Poland

Pages from

149

Pages to

180

Pages count

32

URL

https://www.impan.pl/en/publishing-house/journals-and-series/annales-polonici-mathematici/all/130/2

BibTex

@article{BUT183920,
  author="Veronika {Chrastinová} and Václav {Tryhuk}",
  title="On the Lagrange variational problem",
  journal="Annales Polon.Math.",
  year="2023",
  volume="130",
  number="2",
  pages="149--180",
  doi="10.4064/ap220330-30-1",
  issn="0066-2216",
  url="https://www.impan.pl/en/publishing-house/journals-and-series/annales-polonici-mathematici/all/130/2"
}