论文标题
Kolmogorov操作员在NASH类中与矢量字段
Kolmogorov operator with the vector field in Nash class
论文作者
论文摘要
我们考虑具有可测量均匀椭圆形矩阵的分歧形式抛物线方程和矢量字段，尤其包含$ l^p $，$ p> d $中的向量字段，以及某些不在$ l _ {\ rm loc}^{\ rm loc}^{2+\ varepsilon $ var $ 0中的矢量字段。我们建立了有限的soutions的Hölder连续性，尖锐的两侧高斯在热内核上，Harnack不平等。
We consider divergence-form parabolic equation with measurable uniformly elliptic matrix and the vector field in a large class containing, in particular, the vector fields in $L^p$, $p>d$, as well as some vector fields that are not even in $L_{\rm loc}^{2+\varepsilon}$, $\varepsilon>0$. We establish Hölder continuity of the bounded soutions, sharp two-sided Gaussian bound on the heat kernel, Harnack inequality.
