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 .
Type de document :
Pré-publication, Document de travail
A paraître dans Journal of the European Mathematical Society. 63 pages, 11 figures. 2018
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https://hal.archives-ouvertes.fr/hal-01357047
Contributeur : Cyril Imbert <>
Soumis le : samedi 8 décembre 2018 - 19:04:07
Dernière modification le : jeudi 20 décembre 2018 - 01:28:33

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  • HAL Id : hal-01357047, version 3
  • ARXIV : 1608.07571

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Cyril Imbert, Luis Silvestre. The weak Harnack inequality for the Boltzmann equation without cut-off. A paraître dans Journal of the European Mathematical Society. 63 pages, 11 figures. 2018. 〈hal-01357047v3〉

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