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

Luis Silvestre

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

Analysis of PDEs 2016-04-01 v3

Authors: Luis Silvestre

Abstract

We apply recent results on regularity for general integro-differential equations to derive a priori estimates in H\"older 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.

Keywords

boltzmann equation regularity for elliptic equations gradient estimates

Cite

@article{arxiv.1412.4706,
  title  = {A new regularization mechanism for the Boltzmann equation without cut-off},
  author = {Luis Silvestre},
  journal= {arXiv preprint arXiv:1412.4706},
  year   = {2016}
}

Comments

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

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