Wednesday, September 6, 2023 — 12:00 pm — aula M1.6, edificio Matematica
Existence and asymptotic lower bounds of the fundamental solution of kinetic equation in special relativity
Abstract: We study a class of second order strongly degenerate kinetic operators in the framework of special relativity. More precisely, the operator we consider here is a possible suitable relativistic generalization of the kinetic Fokker-Planck operator. We first describe it as a Hörmander operator which is invariant with respect to Lorentz transformations. We then prove a Lorentz-invariant Harnack type inequality, and we derive sharp asymptotic lower bounds for positive solutions to the equation. As a consequence, we obtain lower bounds for the density of the relativistic stochastic process associated to our operator.
This is a joint work with Francesca Anceschi (Università Politecnica delle Marche) and Sergio Polidoro (Università degli Studi di Modena e Reggio Emilia).