Abstract: 

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

About the Speaker:

Renming Song is a professor in the Department of Mathematics at University of Illinois Urbana-Champaign. His area of Research contains Markov processes, potential theory, stochastic analysis and branching processes.

Homepage: https://faculty.math.illinois.edu/~rsong/