Hamilton-Jacobi Equations and Mean Field Games: From Modeling to Numerics via Analysis

Contribution List

27. TBA

Antonio Siconolfi (Università degli Studi di Roma "La Sapienza")

01/10/2026, 09:30

32. On Hamilton Jacobi equations with time measurable Hamiltonians posed on a 1-dimensional junction

Ariela Briani (Institut Denis Poisson, Université de Tours)

01/10/2026, 10:00

I will describe my recent contribution to the theory of Hamilton-Jacobi equations and optimal control problems posed on networks (see [1]).
I will study evolutive Hamilton–Jacobi equations with Hamiltonians that are discontinuous in time, posed on a simple network consisting of two edges on the real line connected at a single junction. I will introduce a notion of (flux-limited) viscosity...

35. Quantitative vanishing viscosity approximation of fully nonlinear, non-convex, Hamilton-Jacobi equations with Hölder data

Alessandro Goffi (Università di Firenze)

01/10/2026, 10:30

I will discuss new quantitative estimates of the vanishing viscosity process for evolutionary Hamilton-Jacobi PDEs that are neither concave nor convex in the gradient and Hessian entries. I will describe a novel approach that exploits the regularizing properties of sup/inf-convolutions for viscosity solutions combined with the comparison principle. This method provides explicit sharp constants...

30. TBA

Hasnaa Zidani (INSA Rouen Normandie)

01/10/2026, 11:30

24. From Discrete Weak KAM Theory to Computable Aubry–Mather Sets

Cristian Mendico (Université Bourgogne Europe)

01/10/2026, 12:00

Aubry and Mather sets describe the invariant structures selected by action minimization in Hamiltonian dynamics. Their computation is particularly relevant in celestial mechanics, where resonances and transitions between regular and chaotic motion create intricate dynamical patterns that are difficult to detect using trajectories alone.
In this talk, I will present joint work with Fabio...

15. MFG with large discount and agent-based models

Elisa Continelli (Università degli Studi di Padova)

01/10/2026, 12:30

We focus on a class of Mean Field Games with discount. If one assumes that the discount factor is large, these models turn out to behave similarly to agent-based models, where individuals just react to the population distribution according to a given rule. Inspired by a recent work by Bardi and Cardaliaguet, we will elaborate on this connection, showing in particular the uniqueness of...

29. Hamilton-Jacobi equations on Wasserstein spaces

Daniela Tonon (Università degli Studi di Padova)

01/10/2026, 14:30

In this talk, we present a unified approach to Hamilton–Jacobi equations on the Wasserstein space of probability measures arising from deterministic and stochastic dynamics. We introduce a viscosity-solution framework encompassing both first-order equations and semilinear equations driven by idiosyncratic noise. The framework relies on a suitable notion of subdifferential designed to ensure...

12. Building on Lax’s Idea: Quantitative Compactness Estimates for Numerical Solutions of First-Order Nonlinear PDEs

Alessio Basti (Università G. D'Annunzio di Chieti-Pescara)

01/10/2026, 15:00

In my talk, I will discuss recent results on Kolmogorov ε-entropy for numerical approximations of scalar conservation laws and Hamilton-Jacobi equations. The analysis provides quantitative compactness estimates and entropy-transfer principles linking exact and discrete solution sets, yielding an information-theoretic perspective on complexity preservation and the resolution of numerical...

17. Analysis and approximation of first order Mean Field Games with Hamiltonian measurable-in-time and $\mathcal{C}^{1,1}$ in the gradient variable

Valentina Coscetti (Università degli Studi di Roma "La Sapienza")

01/10/2026, 16:00

We present a numerical scheme for a class of first-order,
non-local Mean Field Games systems with two sources of low regularity: the time-dependent data are merely measurable, and the Hamiltonian is only of class $\mathcal{C}^{1,1}$ with respect to the momentum variable. The approach combines a semi-Lagrangian approximation of the Hamilton-Jacobi-Bellman equation with a Lagrange-Galerkin...

14. SLTK: A Semi-Lagrangian ToolKit for PDEs on Unstructured Grids

Simone Cacace (Università degli Studi di Roma "La Sapienza")

01/10/2026, 16:30

In this talk, I will present recent advancements in the development of SLTK, a custom research library designed for the numerical solution of PDEs on complex domains. By employing semi-Lagrangian schemes on unstructured grids, SLTK adapts various techniques from computational geometry and computer graphics to the context of partial differential equations.
Specifically, I will introduce a...

22. Monotonicity Methods for time-dependent Mean Field Games:

Diogo A. Gomes (KAUST)

02/10/2026, 09:00

Abstract. We prove the existence of solutions to first-order, local, time-dependent mean-field games with periodic boundary conditions on the d-dimensional torus. Our approach extends the Banach space monotone operator framework, previously developed for the stationary case, to the substantially harder time-dependent setting. We reformulate the MFG system as a variational inequality for a...

23. Mean Field Games with state constraints and Grushin type dynamics

Paola Mannucci (Università degli Studi di Padova)

02/10/2026, 09:30

We consider a class of finite horizon deterministic mean field games with nonlocal coupling where the agents must follow Grushin type dynamics with state constraints. We require some assumptions on the local interplay between the set of state constraints and the dynamics.

As a first step, we consider the associated optimal control problem and we establish some properties as: the existence...

28. Approximation of deterministic mean field games under state constraints

Francisco J. Silva (Université de Limoges)

02/10/2026, 10:00

In this talk, we study the approximation of equilibria for continuous-time and continuous-space first-order (deterministic) mean field games (Mean Field Games, MFGs) by equilibria of finite MFGs, i.e., games in which the number of time steps and the state space are finite. In the first part, we recall the framework and results obtained in Hadikhanloo–S (2019). In the second part, based on a...

20. Rate of convergence for singular perturbations of Hamilton-Jacobi equations in unbounded spaces

Daria Ghilli (Università di Pavia)

02/10/2026, 10:30

We present rate of convergence results for singular perturbations of Hamilton-Jacobi equations in unbounded spaces where the fast operator is linear, uniformly elliptic and has an Ornstein-Uhlenbeck-type drift. Our achievements are the first rate of convergence results without any periodicity assumption. More in detail, in our HJ equation, the slow operator is a fully nonlinear elliptic...

31. Degenerate second-order PDEs on networks with Kirchhoff conditions

Olivier Ley (INSA de Rennes)

02/10/2026, 11:30

The aim of this talk is to present results concerning nonlinear degenerate elliptic partial differential equations (PDEs) on networks, with Kirchhoff conditions at the vertices. While elliptic PDEs on networks have long been known, Hamilton-Jacobi equations on networks (the case of totally degenerate PDEs) have been the subject of extensive study over the past decade. In recent work conducted...

19. On the null controllability of a degenerate Fokker–Planck equation with a drift term

Genni Fragnelli (Università di Siena)

02/10/2026, 12:00

The Fokker–Planck equation describes the time evolution of the probability density function of the velocity for a particle under the influence of drag forces and random forces. In particular, this equation has multiple applications in information theory, graph theory, data science, finance, economics... In one spatial dimension the Fokker–Planck equation for the probability density $p(t,x)$...

13. Approximation of stable solutions of second order mean field games

Jules Berry (Université Paris-Saclay)

02/10/2026, 12:30

In this talk, we are interested in the stationary MFG system:
\begin{equation}
\begin{cases}
-\Delta u + H(x,Du) + \lambda u = F[m] & \text{in } \mathbb{T}^d, \
-\Delta m - \mathrm{div}(m H_p(x,Du)) + \lambda m = \lambda m_0 & \text{in } \mathbb{T}^d,
\end{cases}
\end{equation}
where $u$ is the value function and $m$ the distribution of the players. Our goal is to establish the...

18. Semi-Lagrangian approximation of viscous transport and conservative equations with one sided Lipschitz velocity fields

Adriano Festa (Politecnico di Torino), Fabio Camilli (Università "G. d'Annunzio" Chieti-Pescara), Dr Luciano Marzufero (Libera Università di Bolzano)

02/10/2026, 14:30

The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the convergence of the schemes, we exploit the characterization of the solution for these equations expressed in terms of measurable time-dependent...

33. Mean convexity and the truncated Laplacian

Martino Bardi (Università degli studi di Padova)

02/10/2026, 15:00

We propose a notion of mean convexity of a function in R^n with respect to all k-dimensional subspaces, k integer between 1 and n. We show its connection with the truncated Laplacian of order k of the function, i.e., the sum of the first k eigenvalues of the Hessian matrix.
We consider the Hessian PDE that prescribes the k-truncated Laplacian, in viscosity sense. We study existence and...