In this paper the question of weak and strong local optimality of a Lipschitz (as opposed to C1 ) extremal is addressed. We show that the classical Jacobi sufficient conditions can be extended to the case of Lipschitz candidates. The key idea for this achievement lies in proving that the “generalized” strengthened Weierstrass condition is equivalent to the existence of a “feedback control” function at which the maximum in the “true” Hamiltonian is attained. Then the Hamilton-Jacobi approach is pursued in order to conclude the result.
