Related papers: Time dependent mean-field games in the superquadra…
The equivalence between logarithmic Sobolev inequalities and hypercontractivity of solutions of Hamilton-Jacobi equations has been proved in [5]. We consider a semi-Lagrangian approximation scheme for the Hamilton-Jacobi equation and we…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…
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 solutions of the problem in the case of a large class of…
In this manuscript, we study a class of linear-quadratic (LQ) mean field control problems with a common noise and their corresponding $N$-particle systems. The mean field control problems considered are not standard LQ mean field control…
In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…
This paper considers linear quadratic (LQ) mean field games with a major player and analyzes an asymptotic solvability problem. It starts with a large-scale system of coupled dynamic programming equations and applies a re-scaling technique…
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…
We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
This work focuses on the rate of convergence for singular perturbation problems for first-order Hamilton-Jacobi equations. As an application we derive the rate of convergence for singularly perturbed two-players zero-sum deterministic…
Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi equations with a super-quadratic growth in the gradient variable are proved to be H\"older continuous, with a modulus depending only on the growth of the…
In this note we propose a transformation which decouples stationary Mean Field Games systems with superlinear Hamiltonians of the form |p|^r, and turns the Hamilton-Jacobi-Bellman equation into a quasi-linear equation involving the…
We study the large time behavior of Lipschitz continuous, possibly unbounded, viscosity solutions of Hamilton-Jacobi Equations in the whole space $\R^N$. The associated ergodic problem has Lipschitz continuous solutions if the analogue of…
In this paper we provide the existence of classical solutions to stationary mean field game systems in the whole space $\mathbb{R}^N$, with coercive potential, aggregating local coupling, and under general conditions on the Hamiltonian,…
We study continuous dependence estimates for viscous Hamilton- Jacobi equations defined on a network Gamma. Given two Hamilton-Jacobi equations, we prove an estimate of the C2-norm of the difference between the corresponding solutions in…
We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the…
This paper introduces a notion of weak solution for the coupled system of master equations in mean field games with a major player. It extends the previously introduced notion of Lipschitz solutions in mean field games. By relying on a…
We consider the simplest example of a time-dependent first order Hamilton-Jacobi equation, in one space dimension and with a bounded and Lipschitz continuous Hamiltonian which only depends on the spatial derivative. We show that if the…
We analyze asymptotic convergence properties of Newton's method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean…
We study the regularity and well-posedness of the local, first-order forward-backward mean field games system, assuming a polynomially growing cost function and a Hamiltonian of quadratic growth. We consider systems and terminal data that…