53 citations · 54 across the 3 of their papers we have counts for
5 papers
The planning problem in Mean Field Games as regularized mass transport
P. Jameson Graber, Alpár R. Mészáros, Francisco J. Silva +1
In this paper, using variational approaches, we investigate the first order planning problem arising in the theory of mean field games. We show the existence and uniqueness of weak…
On nonlinear cross-diffusion systems: an optimal transport approach
Inwon Kim, Alpár R. Mészáros
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flo…
On the variational formulation of some stationary second order mean field games systems
Alpár Richárd Mészáros, Francisco J. Silva
We consider the variational approach to prove the existence of solutions of second order stationary Mean Field Games on a bounded domain , with Neumann b…
First order Mean Field Games with density constraints: Pressure equals Price
Pierre Cardaliaguet, Alpár Richárd Mészáros, Filippo Santambrogio
In this paper we study Mean Field Game systems under density constraints as optimality conditions of two optimization problems in duality. A weak solution of the system contains an…
BV Estimates in Optimal Transportation and Applications
Guido De Philippis, Alpár Mészáros, Filippo Santambrogio +1
In this paper we study the BV regularity for solutions of variational problems in Optimal Transportation. As an application we recover BV estimates for solutions of some non-linear…