The weak Harnack inequality for the Boltzmann equation without cut-off
Analysis of PDEs
2019-02-22 v3
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.
Keywords
Cite
@article{arxiv.1608.07571,
title = {The weak Harnack inequality for the Boltzmann equation without cut-off},
author = {Cyril Imbert and Luis Silvestre},
journal= {arXiv preprint arXiv:1608.07571},
year = {2019}
}
Comments
In this third arXiv version, we adjusted the cancellation assumption (1.7) in a way that affects the case s=1/2 only