Time dependent mean-field games in the superquadratic case

Understand

We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure.

• Such problems pose substantial mathematical challenges as the key techniques used in the subquadratic case do not extend to the superquadratic setting.
• Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton-Jacobi equation are obtained through a novel set of techniques.
• These explore the parabolic nature of the problem through the non-linear adjoint method.