I will discuss a mean field game model on the synchronization of coupled oscillators, initially proposed by Yin, Mehta, Meyn, and Shanbhag, and recently examined by Carmona, Cormier, and Soner. This m...
Schrödinger-type equations model a lot of natural phenomena and their solutions have interesting and important properties. This gives rise to the search for normalised solutions, i.e., when the mass i...
We discuss the unique continuation property for linear differential operators of the form sum of squares of vector fields satisfying Hörmander's bracket generating condition. We provide some negative ...
Nash systems are strongly coupled systems of semilinar parabolic equations that describe closed-loop Nash equilibria in stochastic differential games. Despite existence, uniqueness and regularity for ...
We analyze the problem of controlling a multiagent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with a...
We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actua...
In this talk we consider a class of scalar nonlinear models describing crowd dynamics. The congestion term appears in the transport equation in the form of a compactly supported nonlinear mobility fun...
In this talk I will present a recent work in which the strong ill-posedness of the two-dimensional Boussinesq system is proven. I will show explicit examples of initial data with vorticity and densit...
The classical Stepanov theorem strengthens the Rademacher theorem by establishing almost-everywhere differentiability for pointwise Lipschitz functions into Euclidean spaces. In this seminar, I will d...
In a recent paper, we study the long--time behavior and the stability of the surface diffusion flow of smooth hypersurfaces in the flat torus \(\mathbb T^n\). According to this flow, smooth hypersurfa...
