33 citations · 120 across the 40 of their papers we have counts for
7 papers · 1 filter
Existence and non-existence for time-dependent mean field games with strong aggregation
Marco Cirant, Daria Ghilli
We investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings of the form , ,…
Comparison principles by monotonicity and duality for constant coefficient nonlinear potential theory and PDEs
Marco Cirant, F. Reese Harvey, H. Blaine Lawson +1
We prove comparison principles for nonlinear potential theories in euclidian spaces in a very straightforward manner from duality and monotonicity. We shall also show how to deduce…
Maximal -regularity for parabolic Hamilton-Jacobi equations and applications to Mean Field Games
Marco Cirant, Alessandro Goffi
In this paper we investigate maximal -regularity for time-dependent viscous Hamilton-Jacobi equations with unbounded right-hand side and superlinear growth in the gradient. Ou…
-dimensional multi-agent optimal control with aggregation and distance constraints: qualitative properties and mean-field limit
Annalisa Cesaroni, Marco Cirant
In this paper we consider an optimal control problem for a large population of interacting agents with deterministic dynamics, aggregating potential and constraints on reciprocal d…
Comparison principles for viscosity solutions of elliptic branches of fully nonlinear equations independent of the gradient
Marco Cirant, Kevin R. Payne
The validity of the comparison principle in variable coefficient fully nonlinear gradient free potential theory is examined and then used to prove the comparison principle for full…
Splitting methods and short time existence for the master equations in mean field games
Pierre Cardaliaguet, Marco Cirant, Alessio Porretta
We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, d…
On the problem of maximal -regularity for viscous Hamilton-Jacobi equations
Marco Cirant, Alessandro Goffi
For , we prove that maximal regularity of type holds for periodic solutions to in , under the (sharp) assumption $q > d \frac{γ-1}γ…