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arXiv · 1506.01908

H\"{o}lder regularity for hypoelliptic kinetic equations with rough diffusion coefficients

François Golse·Alexis Vasseur
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Abstract

This paper is dedicated to the application of the DeGiorgi-Nash-Moser regularity theory to the kinetic Fokker-Planck equation. This equation is hypoelliptic. It is parabolic only in the velocity variable, while the Liouville transport operator has a mixing effect in the position/velocity phase space. The mixing effect is incorporated in the classical DeGiorgi method via the averaging lemmas. The result can be seen as a H\"{o}lder regularity version of the classical averaging lemmas.

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François Golse, Alexis Vasseur. 2015-06-05. H\"{o}lder regularity for hypoelliptic kinetic equations with rough diffusion coefficients. https://arxiv.org/abs/1506.01908

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