## New preprint about the Boltzmann equation

We wrote with Luis Silvestre a paper entitled « Weak Harnack inequality for the Boltzmann equation without cut-off ». See arxiv and hal.

Abstract: « In this paper, we obtain the weak Harnack inequality and H\ »older estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cut-off can be written in this form and satisfies our assumptions provided that the mass density is bounded away from vacuum and mass, energy and entropy densities are bounded above. As a consequence, we derive a local H\ »older estimate and a quantitative lower bound for solutions of the (inhomogeneous) Boltzmann equation without cut-off. »