Noether’s theorem for non-smooth extremals of variational problems with time delay
Gastão S.F. Frederico, Tatiana Odzijewicz, Delfim F.M. Torres · Applicable Analysis · 2013
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.