Speaker: Panki Kim

Title: On Markov processes with singular jumping measures

Abstract: In this talk, we discuss some potential theory of symmetric Markov process with singular jumping measure. An example of such processes is symmetric Markov process in a subset of Euclidean space  whose jump kernel is $J(x,y)=|x-y|^{-d-\alpha}B(x,y)$, where $\alpha\in (0, 2)$ and $B(x,y)$ can blow up to infinity at the boundary. We discuss the H\"older regularity, Harnack and boundary Harnack principle and sharp two-sided estimates on the Green function.

This talk  is based on joint works with Soobin Cho (University of Illinois, USA),  Renming Song (University of Illinois, USA) and Zoran Vondra\v{c}ek (University of Zagreb, Croatia).