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Journal Articles Journal of the European Mathematical Society Year : 2020

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

Abstract

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 .
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Dates and versions

hal-01357047 , version 1 (30-08-2016)
hal-01357047 , version 2 (02-08-2017)
hal-01357047 , version 3 (08-12-2018)

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Cite

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⟩
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