報告人：宋仁明 教授

報告題目：Heat kernel estimates for Markov processes with jump kernels blowing-up at the boundary

報告時間：2026年1月5日（周一）16:00-17:00

報告地點：云龍校區6號樓304報告廳

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

宋仁明，美國Illinois大學教授，1986年河北大學碩士畢業，1989年美國Florida大學博士畢業。訪問過德國、法國、日本、韓國等國家和臺灣地區的20余所大學和研究所。從事隨機過程和隨機分析研究，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.》等數學、概率國際權威刊物上發表論文160余篇；多次在國際學術會議上作邀請報告。

報告摘要：

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.