报告人：宋仁明 教授
报告题目：Heat kernel estimates for Markov processes with jump kernels blowing-up at the boundary
报告时间：2026年1月5日（周一）16:00-17:00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
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、韩国等国家和台湾地区的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。
报告摘要：
In this talk, I will present some recent results about purely discontinuous symmetric Markov processes on closed subsets of ${\mathbb R}^d$, $d\ge 1$, 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 the state space. 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 sharp two-sided heat kernel estimates for these Markov processes. A fundamental difficulty in accomplishing this task is that, in contrast to the existing literature on heat kernels for jump processes, the tails of the associated jump measures in our setting are not uniformly bounded. Thus, standard techniques in the existing literature used to study heat kernels are not applicable.To overcome this obstacle, we employ recently developed weighted functional inequalities specifically designed for jump kernels blowing up at the boundary. This talk is based on a joint paper with Soobin Cho, Panki Kim and Zoran Vondracek.
