The weak Harnack inequality for the Boltzmann equation without cut-off

Cyril Imbert (1) , Luis Silvestre (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 Department of Mathematics [Chicago]

We obtain the weak Harnack inequality and Hölder estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cutoff 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 Hölder estimate and a quantitative lower bound for solutions of the (inhomogeneous) Boltzmann equation without cutoff .

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Luis Silvestre. The weak Harnack inequality for the Boltzmann equation without cut-off. Journal of the European Mathematical Society, 2020, 22 (2), pp. 507-592. ⟨10.4171/JEMS/928⟩. ⟨hal-01357047v3⟩