Tuesday, January 20, 2026 — 4:00 pm — aula M1.5, edificio Matematica
Trajectory methods in kinetic theory
Abstract: In this talk, we focus on the study of a class of kinetic equations, whose prototype is the following Fokker-Planck equation
$$\Delta_vf(v,x,t)+ v \cdot \nabla_x u(v,x,t) – \partial_t f(v,x,t)=s(v,x,t),$$
where $(v,x,t) \in \mathbb{R}^{2n+1}$. Through a “trajectory” approach, we prove a Poincaré inequality for weak solutions, a keystone for the study of the weak regularity theory and the consequent proof of a weak Harnack inequality.
The talk is based on a joint work in collaboration with Dietert, Guerand, Loher, Mouhot and Rebucci.