Potential theory of Dirichlet forms degenerate at the boundary
[Math. Dept.]
November 10, 2020 09:30-10:30
腾讯会议（线上）
ID: 455 133 487 Password: 23579
SPEAKER
Renming Song (University of Illinois at Urbana-Champaign & Sichuan University)
ABSTRACT
In this talk I will present some recent results on the potential theory of Markov processes with jump kernels degenerate at the boundary of its state space $R^d_+$, the upper half space of $R^d$. The jump kernel is of the form $J^D(x, )=|x-y|^{-d-\alpha}B(x, y)$, where $\alpha\in (0, 2)$ and $B(x, y)$, which involves three parameters $\beta_1, \beta_2$ and $\beta_2$, tends to 0 when $x$ or $y$ tends to the boundary. We assume that the killing function is of the form $\kappa(x)=cx_d^{-\alpha}$. Our main results are sharp two-sided estimates on the Green functions of these processes. As applications of the green function estimates, we show that the boundary Harnack principle holds for certain region of the parameters and fails in the other region. This talk is based on two joint papers with Panki Kim and Zoran Vondracek.
SUPPORTED BY
Tianyuan Mathematical Center in Southwest China
School of Mathematics, Sichuan University
VIDEO
- Potential theory of Dirichlet forms degenerate at the boundary
- 09:30 - 10:30, 2020-11-10 at 腾讯会议（线上）
- Renming Song (University of Illinois at Urbana-Champaign & Sichuan University)