Boundary Harnack Principle for Critical Fractional Laplacian with Drift
主 题: Boundary Harnack Principle for Critical Fractional Laplacian with Drift
报告人: 王龙敏 副教授 (南开大学)
时 间: 2014-03-03 15:00-16:00
地 点: welcome欢迎光临威尼斯公司理科一号楼 1493（概率论系列报告）
Let $d \geq 2$ and $b$ a H\"older continuous vector field on ${\mathbb R}^d$. In this talk, we will prove the boundary Harnack principle with explicit rate for $-(-\Delta)^{1/2} + b \cdot \nabla$ in a bounded $C^{1,1}$ open set $D \subset \mathbb{R}^d$ under some regularity assumptions on $b$. The rate depends on the boundary value of drift $b$ and equals to $1/2$ only when $b$ is tangent to the boundary $\partial D$. As an application, we will establish the sharp two-sided estimates for the Green function of $-(-\Delta)^{1/2} + b \cdot \nabla$ in $D$ with zero exterior condition. In general, the Green function is also not comparable to that of unperturbed operator $-(-\Delta)^{1/2}$. The talk is based on joint work with Zhen-Qing Chen.
