  We consider deterministic mean field games in which the agents control their
acceleration and are constrained to remain in a domain of R n. We study relaxed
equilibria in the Lagrangian setting; they are described by a probability
measure on trajectories. The main results of the paper concern the existence of
relaxed equilibria under suitable assumptions. The fact that the optimal
trajectories of the related optimal control problem solved by the agents do not
form a compact set brings a difficulty in the proof of existence. The proof
also requires closed graph properties of the map which associates to initial
conditions the set of optimal trajectories.
