Renming Song : Potential theory of Dirichlet forms with jump kernels blowing up at the boundary

Posted by Cheng Ouyang , part of the Statistics and Data Science Seminar.

At

Oct. 12, 2022, 4 p.m.

In

636 SEO

Abstract

In this talk, I will present some recent results on potential theory of Dirichlet forms on the half-space $\mathbb{R}^d_+$ defined by the jump kernel $J(x,y)=|x-y|^{-d-\alpha}{\cal B}(x,y)$, where $\alpha\in (0,2)$ and ${\cal B}(x,y)$ can blow up to infinity at the boundary. The main results include boundary Harnack principle and sharp two-sided Green function estimates. This talk is based on a joint paper with Panki Kim and Zoran Vondracek.