Related papers: Quantitative maximal $L^2$-regularity for viscous …
In this paper, we prove the existence of classical solutions for second order stationary mean-field game systems. These arise in ergodic (mean-field) optimal control, convex degenerate problems in calculus of variations, and in the study of…
In this paper we investigate maximal $L^q$-regularity for time-dependent viscous Hamilton-Jacobi equations with unbounded right-hand side and superlinear growth in the gradient. Our approach is based on the interplay between new integral…
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…
This work is devoted to the studies of a Hamilton--Jacobi equation with a quadratic and degenerate Hamiltonian, which comes from the dynamics of a multipeakon in the Camassa--Holm equation. It is given by a quadratic form with a singular…
In this paper, we consider a class of infinitely degenerate partial differential systems to obtain the Nash equilibria in the mean field games. The degeneracy in the diffusion and the Hamiltonian may be different. This feature brings…
We establish local H\"older estimates for viscosity solutions of fully nonlinear second order equations with quadratic growth in the gradient and unbounded right-hand side in $L^q$ spaces, for an integrability threshold $q$ guaranteeing the…
We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as the key techniques used in the subquadratic case do not extend…
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…
We study the existence of classical solutions to a broad class of local, first order, forward-backward Extended Mean Field Games systems, that includes standard Mean Field Games, Mean Field Games with congestion, and mean field type control…
Motivated by parallels between mean field games and random matrix theory, we develop stochastic optimal control problems and viscosity solutions to Hamilton-Jacobi equations in the setting of non-commutative variables. Rather than real…
We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents…
We show in this paper that maximal $L^q$-regularity for time-dependent viscous Hamilton-Jacobi equations with unbounded right-hand side and superquadratic $\gamma$-growth in the gradient holds in the full range $ q >…
We provide an approximation scheme for first-order stationary mean field games with a separable Hamiltonian. First, we discretize Hamilton-Jacobi equations by discretizing in time, and then prove the existence of minimizing holonomic…
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, and relies on the analysis of the regularity of…
We study first order evolutive Mean Field Games where the Hamiltonian is non-coercive. This situation occurs, for instance, when some directions are "forbidden" to the generic player at some points. We establish the existence of a weak…
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the…
We obtain space-time H\"older regularity estimates for solutions of first- and second-order Hamilton-Jacobi equations perturbed with an additive stochastic forcing term. The bounds depend only on the growth of the Hamiltonian in the…
We establish the existence and uniqueness of weak and renormalized solutions to a degenerate, hypoelliptic Mean Field Games system with local coupling. An important step is to obtain $L^{\infty}-$bounds for solutions to a degenerate…
We search for non-constant normalized solutions to the semilinear elliptic system \[ \begin{cases} - \nu \Delta v_i + g_i(v_j^2) v_i = \lambda_i v_i,\quad v_i>0 & \text{in $\Omega$} \\ \partial_n v_i = 0 & \text{on $\partial \Omega$}\\…
We consider the variational approach to prove the existence of solutions of second order stationary Mean Field Games on a bounded domain $\Omega\subseteq \mathbb{R}^{d}$, with Neumann boundary conditions, and with and without density…