A-PRIORI ESTIMATES FOR STATIONARY MEAN-FIELD GAMES
Por:
Gomes D.A., Pires G.E., Sánchez-Morgado H.
Publicada:
1 jun 2012
Resumen:
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 W-1,W- 2 estimates for the value function u and that the players distribution m satisfies root m is an element of W-1,W- 2. We discuss further results for power-like nonlinearities and prove higher regularity if the space dimension is 2. In particular we also obtain in this last case W-2,W-p estimates for u.
Filiaciones:
Gomes D.A.:
Departamento de Matemática and CAMGSD, IST, Avenida Rovisco Pais, Lisboa, Portugal
Pires G.E.:
Departamento de Matemática and CAMGSD, IST, Avenida Rovisco Pais, Lisboa, Portugal
Sánchez-Morgado H.:
Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico
Hybrid Gold
|