### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Royal Society of Edinburgh - Proceedings A*,

*132*(6), 1361-1371.

**On conservation laws and necessary conditions in the calculus of variations.** / Francfort, G.; Sivaloganathan, J.

Research output: Contribution to journal › Article

*Royal Society of Edinburgh - Proceedings A*, vol. 132, no. 6, pp. 1361-1371.

}

TY - JOUR

T1 - On conservation laws and necessary conditions in the calculus of variations

AU - Francfort, G.

AU - Sivaloganathan, J.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036974568&partnerID=8YFLogxK

M3 - Article

VL - 132

SP - 1361

EP - 1371

JO - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

SN - 0308-2105

IS - 6

ER -