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On conservation laws and necessary conditions in the calculus of variations

Published online by Cambridge University Press:  12 July 2007

G. Francfort  and
J. Sivaloganathan
G. Francfort
Affiliation:
LPMTM, Université Paris 13, 93430 Villetaneuse, France
J. Sivaloganathan
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
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Abstract

It is well known from the work of Noether that every variational symmetry of an integral functional gives rise to a corresponding conservation law. In this paper, we prove that each such conservation law arises directly as the Euler-Lagrange equation for the functional on taking suitable variations around a minimizer.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 6 , December 2002 , pp. 1361 - 1371
Copyright
Copyright © Royal Society of Edinburgh 2002

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