In this paper we establish a new class of a-priori estimates for stationary mean-field games which have a quasi-variational structure. In particular we prove W1,2 estimates for the value function u and that the players distribution m satises √W1,2We discuss further results for powerlike nonlinearities and prove higher regularity if the space dimension is 2. In particular we also obtain in this last case W2,p estimates for u.
- A-priori estimates
- Mean field games
- Variational and quasi-variational methods
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Applied Mathematics