论文标题
带有通用运算符和粗糙系数的动力学福克 - 普兰克方程的速度平均和Hölder规律性
Velocity averaging and Hölder regularity for kinetic Fokker-Planck equations with general transport operators and rough coefficients
论文作者
论文摘要
本文介绍了具有通用运输算子和粗糙系数的动力学福克 - 普兰克方程弱解决方案的局部界限和Hölder连续性。这些结果是由于扩散和运输的混合作用。尽管该方程仅在速度变量中是抛物线，但只要传输部分$ \ partial_t+b（v）\ cdot \ nabla_x $在某种意义上是非重新等级的，它具有低纤维化结构。我们通过重新审视Golse，Imbert，Mouhot和Vasseur提出的方法来实现结果，以$ b（v）= v $，将椭圆形的giorgi-nash-moser理论与速度平均相结合。
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.
