On uniqueness in evolution quasivariational inequalities

We consider a rate independent evolution quasi variational inequality in a Hilbert space X with closed convex constraints having nonempty interior. We prove that there exists a unique solution which is Lipschitz dependent on the data, if the dependence of the Minkowski functional on the solution is Lipschitzian with a small constant and if also the gradient of the square of the Minkowski functional is Lipschitz continuous with respect to all variables. We exhibit an example of nonuniqueness if the assumption of Lipschitz continuity is violated by an arbitrarily small degree.