### 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.

Original language | English |
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Pages (from-to) | 1361-1371 |

Number of pages | 11 |

Journal | Royal Society of Edinburgh - Proceedings A |

Volume | 132 |

Issue number | 6 |

Publication status | Published - 2002 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Francfort, G., & Sivaloganathan, J. (2002). On conservation laws and necessary conditions in the calculus of variations.

*Royal Society of Edinburgh - Proceedings A*,*132*(6), 1361-1371.