SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2746-2775, January 2021.
This article addresses the local boundedness and Hölder continuity of weak solutions to kinetic Fokker--Planck equations with general transport operators and rough coefficients. These results are due to the mixing effect of diffusion and transport. Although the equation is parabolic only in the velocity variable, it has a hypoelliptic structure provided that the transport part $\partial_t+b(v)\cdot\nabla_x$ is nondegenerate in some sense. We achieve the results by revisiting the method, proposed by Golse, Imbert, Mouhot, and Vasseur in the case $b(v)= v$, that combines the elliptic De Giorgi--Nash--Moser theory with velocity averaging lemmas.

中文翻译：

---

具有一般输运算子和粗糙系数的动力学Fokker-Planck方程的速度平均和Hölder规律

SIAM数学分析杂志，第53卷，第3期，第2746-2775页，2021年1月。
本文讨论了具有一般输运算子和粗糙系数的动力学Fokker-Planck方程弱解的局部有界性和Hölder连续性。这些结果归因于扩散和运输的混合效应。尽管该方程仅在速度变量中是抛物线的，但只要传输部分$ \ partial_t + b（v）\ cdot \ nabla_x $在某种意义上是简并的，它就具有椭圆的结构。我们通过回顾由Golse，Imbert，Mouhot和Vasseur在$ b（v）= v $情况下提出的方法实现结果，该方法将椭圆形De Giorgi-Nash-Moser理论与速度平均引理结合在一起。