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 Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/4100

title: Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations
authors: Torres, D.F.M.
keywords: Calculus of variations
DuBois-Reymond extremals
Euler-Lagrange extremals
Higher-order variational problems
Lipschitz admissible functions
Noether's theorem
issue date: 2004
publisher: American Institute of Mathematical Sciences (AIMS)
abstract: For nonsmooth Euler-Lagrange extremals, Noether's conservation laws cease to be valid. We show that Emmy Noether's theorem of the calculus of variations is still valid in the wider class of Lipschitz functions, as long as one restrict the Euler-Lagrange extremals to those which satisfy the DuBoisReymond necessary condition. In the smooth case all Euler-Lagrange extremals are DuBois-Reymond extremals, and the result gives a proper extension of the classical Noether's theorem. This is in contrast with the recent developments of Noether's symmetry theorems to the optimal control setting, which give rise to non-proper extensions when specified for the problems of the calculus of variations. Results are also obtained for variational problems with higher-order derivatives.
URI: http://hdl.handle.net/10773/4100
ISSN: 1534-0392
source: Communications on Pure and Applied Analysis
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