Bakry-Emery meet Villani

Abstract

We revisit Villani's approach to the study of hypocoercive diffusion operators by applying a variant of the Bakry-Émery machinery. The method relies on a generalized Bakry-Émery type criterion that applies to Kolmogorov type operators. Our approach includes as a special case the kinetic Fokker-Planck equation and allows, in that case, to recover hypocoercive estimates first obtained by Villani.

arXiv commentTo appear in Journal of Functional Analysis. Section 3 has been removed. Section 2.6 is taken from arXiv:1602.04177. The preprint arXiv:1602.04177 will be not be published, but only used as lecture notes