On the Existence and Uniqueness of Solutions to Time-Dependent Fractional MFG

  title={On the Existence and Uniqueness of Solutions to Time-Dependent Fractional MFG},
  author={Marco Cirant and Alessandro Goffi},
  journal={SIAM J. Math. Anal.},
We establish existence and uniqueness of solutions to evolutive fractional mean field game systems with regularizing coupling for any order of the fractional Laplacian $s\in(0,1)$. The existence is... 
On fully nonlinear parabolic mean field games with examples of nonlocal and local diffusions
We prove existence and uniqueness of solutions of a class of abstract fully nonlinear mean field game systems. We justify that such problems are related to controlled local or nonlocal diffusions, orExpand
On an optimal control problem of time-fractional advection-diffusion equation
We consider an optimal control problem of an advection-diffusion equation with Caputo time-fractional derivative. By convex duality method we obtain as optimality condition a forward-backward coupledExpand
Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative
We study existence, uniqueness and regularity properties of classical solutions to viscous Hamilton–Jacobi equations with Caputo time-fractional derivative. Our study relies on a combination of aExpand
Variational Time-Fractional Mean Field Games
The theory of variational MFG is extended to the subdiffusive situation in which the individual agent follows a non-Markovian dynamics given by a subdiffusion process. Expand
Lipschitz regularity for viscous Hamilton-Jacobi equations with L terms
We provide Lipschitz regularity for solutions to viscous time-dependent Hamilton-Jacobi equations with right-hand side belonging to Lebesgue spaces. Our approach is based on a duality method, andExpand
A P ] 2 J ul 2 01 9 Variational time-fractional Mean Field Games
We consider the variational structure of a time-fractional second order Mean Field Games (MFG) system. The MFG system consists of time-fractional Fokker-Planck and Hamilton-JacobiBellman equations.Expand
On Classical Solutions Of Time-Dependent Fractional Mean Field Game Systems
In this paper we study parabolic Mean Field Game systems with nonlocal/fractional diffusion. Such models come from games where the noise is non-Gaussian and the resulting controlled diffusion processExpand
A policy iteration method for mean field games
This paper introduces a policy iteration method for Mean Field Games systems and shows the convergence of this procedure to a solution of the problem, and introduces suitable discretizations to numerically solve both stationary and evolutive problems. Expand
Maximal $$L^q$$-Regularity for Parabolic Hamilton–Jacobi Equations and Applications to Mean Field Games
In this paper we investigate maximal $$L^q$$ L q -regularity for time-dependent viscous Hamilton–Jacobi equations with unbounded right-hand side and superlinear growth in the gradient. OurExpand
On Numerical approximations of fractional and nonlocal Mean Field Games
The methods are monotone, stable, and consistent, and they prove convergence along subsequences for (i) degenerate equations in one space dimension and (ii) nondegenerates equations in arbitrary dimensions. Expand


Mean field games systems of first order
We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of theExpand
On non-uniqueness and uniqueness of solutions in finite-horizon Mean Field Games
This paper presents a class of evolutive Mean Field Games with multiple solutions for all time horizons T and convex but non-smooth Hamiltonian H, as well as for smooth H and T large enough. TheExpand
We prove global Sobolev regularity and pointwise upper bounds for transition densities associated with second order differential operators in R N with unbounded drift. As an application, we obtainExpand
Regularity of solutions to the parabolic fractional obstacle problem
In this paper we study a parabolic version of the fractional obstacle problem, proving almost optimal regularity for the solution. This problem is motivated by an American option model proposed byExpand
Short-Time Existence for a General Backward–Forward Parabolic System Arising from Mean-Field Games
The local in time existence of a regular solution of a nonlinear parabolic backward–forward system arising from the theory of mean-field games is studied and applied to very general MFG models, including also congestion problems. Expand
Uniqueness of solutions in Mean Field Games with several populations and Neumann conditions
We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness ofExpand
Sobolev regularity for the first order Hamilton–Jacobi equation
We provide Sobolev estimates for solutions of first order Hamilton–Jacobi equations with Hamiltonians which are superlinear in the gradient variable. We also show that the solutions areExpand
On stationary fractional mean field games
Abstract We provide an existence result for stationary fractional mean field game systems, with fractional exponent greater than 1/2. In the case in which the coupling is a nonlocal regularizingExpand
On the abstract Cauchy problem of parabolic type in spaces of continuous functions
On etudie l'existence, l'unicite et les proprietes de regularite des solutions du probleme de Cauchy u'(t)=Au(r)+f(t), o<t≤T, u(O)=U 0 ou A:D A CE→E est un operateur lineaire clos dans l'espace deExpand
Second order mean field games with degenerate diffusion and local coupling
We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformlyExpand