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

  • Cyril Imbert

    École Normale Supérieure, Paris, France
  • Luis Silvestre

    University of Chicago, USA
The weak Harnack inequality for the Boltzmann equation without cut-off cover

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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 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 Hölder estimate and a quantitative lower bound for solutions of the (inhomogeneous) Boltzmann equation without cut-off.

Cite this article

Cyril Imbert, Luis Silvestre, The weak Harnack inequality for the Boltzmann equation without cut-off. J. Eur. Math. Soc. 22 (2020), no. 2, pp. 507–592

DOI 10.4171/JEMS/928