On the relativistic Fokker-Planck operator

We study a class of second order strongly degenerate kinetic operators L in the framework of special relativity. More precisely, the operator L we consider here is a possible suitable relativistic generalization of the kinetic Fokker-Planck operator. We first describe L as a Hormander operator which is invariant with respect to Lorentz trans- formations. We then prove a Lorentz-invariant Harnack type inequality, and we derive accurate asymptotic lower bounds for positive solutions to L f = 0. As a consequence, we obtain lower bounds for the density of the relativistic stochastic process associated to L . This is a joint work with Francesca Anceschi (Università Politecnica delle Marche) and Sergio Polidoro (Università degli Studi di Modena e Reggio Emilia).