报告题目：Potential theory of Markov processes with jump kernels blowing up at the boundary
时 间：2026年05月27日（星期三）10：00
地 点：理工南楼621
主 办：数学与统计学院
参加对象：相关专业师生
报告摘要：In these talk, I will give a survey of some recent results about purely discontinuous symmetric Markov processes on subsets $D$ of ${\mathbb R}^d$ with jump kernels of the form $J(x,y)=|x-y|^{-d-\alpha}{\mathcal B}(x,y)$, $\alpha\in (0,2)$, where the function ${\mathcal B}(x,y)$ may blow up at the boundary of $D$. We study both conservative Markov processes of this type and critically killed Markov processes of this type. Examples of Markov processes that fall into our general framework include traces of isotropic $\alpha$-stable processes in $C^{1,\rm Dini}$ sets, processes in Lipschitz sets arising in connection with the nonlocal Neumann problem, and a large class of resurrected self-similar processes in the closed upper half-space. Our main results are boundary Harnack principle, sharp two-sided heat kernel estimates and sharp two-sided Green function estimates for these Markov processes. This talk is based on some recent joint works with Soobin Cho, Panki Kim and Zoran Vondracek.
报告人简介：宋仁明，美国Illinois大学教授，1986年河北大学硕士毕业，1989年美国Florida大学博士毕业。访问过德国、法国、日本、韩国和台湾等国家和地区的20余所大学和研究所。从事随机过程和随机分析研究，在《Trans. Amer. Math. Soc.》、《Proc. London Math. Soc.》、《J. European Math. Soc》、《Math. Ann.》、《J. Funct. Anal.》、《Ann. Probab.》、《Probab. Th. Rel. Fields》、《Stoch. Proc. Appl.》等数学、概率国际权威刊物上发表论文160余篇；多次在国际学术会议上作邀请报告。