A new regularization mechanism for the Boltzmann equation without cut-off

Abstract

We apply recent results on regularity for general integro-differential equations to derive a priori estimates in Hölder spaces for the space homogeneous Boltzmann equation in the non cut-off case. We also show an a priori estimate in $L^{\infty }$ which applies in the space inhomogeneous case as well, provided that the macroscopic quantities remain bounded.

A few typos fixed and a reference added. Note that in the first revision we removed Corollary 1.4 from the first version of the paper

References in corpus (2)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Regularity for fully nonlinear nonlocal parabolic equations with rough kernels