Noether's theorem for non-smooth extremals of variational problems with time delay

Abstract

We obtain a non-smooth 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. © 2013 Taylor & Francis.