Non-coercive first order Mean Field Games

I will talk about two joint works with Y. Achdou, C. Marchi, C. Mariconda e N. Tchou.
We study first order evolutive Mean Field Games (MFG) where the Hamiltonian is non-coercive.
First of all I will describe the classical results about the existence of a solution of the MFG system when the Hamiltonian is coercive. Then I will show our results on two different models where the Hamiltonian is degenerate: the first is the case where the generic player has "forbidden" some directions at some points, the second where the player has to control its acceleration.