Hypoellipticity for a class of kinetic equations

Abstract

In this work, we study a class of operators coming from the linearization of some kinetic equations such as Boltzmann equations and Vlasov-Fokker-Planck equations. Since it is not a standard class of pseudo-differential operators, we obtain hypoelliptic estimates in some weight functions space and show the regularity of weak solutions for linear and semilinear equations.