Noether's Theorem for Nonsmooth Extremals of Variational Problems with Time Delay

2012/12/20 by Gastao S. F. Frederico, Tatiana Odzijewicz, Delfim F. M. Torres · 1 citation
Mathematics · Physics and Astronomy · #math.OC #math-ph #math.MP #msc:49K05 #msc:49S05

paper · pdf · doi:10.1080/00036811.2012.762090

published as Applicable Analysis 93 (2014), no. 1, 153--170 · This is a preprint of a paper whose final and definite form will be published in Applicable Analysis. Manuscript submitted 07-Nov-2012; accepted for publication 19-Dec-2012

arxiv created 2012/12/20 · arxiv updated 2014/02/11

Abstract

We obtain a nonsmooth extension of Noether's symmetry theorem for variational problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions, as long as the delayed Euler-Lagrange extremals are restricted to those that satisfy the DuBois-Reymond necessary optimality condition. The important case of delayed variational problems with higher-order derivatives is considered as well.

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• Hight-order Noether's Theorem for Nonsmooth Extremals of Isoperimetric Variational Problems with Time Delay

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