On conservation laws and necessary conditions in the calculus of variations
Published online by Cambridge University Press: 12 July 2007
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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