Hölder Regularity for Hypoelliptic Kinetic Equations with Rough Diffusion Coefficients

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 Hölder regularity version of the classical averaging lemmas.
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https://hal-polytechnique.archives-ouvertes.fr/hal-01160566
Contributor : François Golse <>
Submitted on : Monday, June 15, 2015 - 1:40:09 AM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM
Long-term archiving on : Tuesday, September 15, 2015 - 2:16:12 PM

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  • HAL Id : hal-01160566, version 2

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François Golse, Alexis Vasseur. Hölder Regularity for Hypoelliptic Kinetic Equations with Rough Diffusion Coefficients. 2015. ⟨hal-01160566v2⟩

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