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On conservation laws and necessary conditions in the calculus of variations

  • G. Francfort (a1) and J. Sivaloganathan (a2)


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.



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