報(bào)告人：宋仁明 教授
報(bào)告題目：Heat kernel estimates for Markov processes with jump kernels blowing-up at the boundary
報(bào)告時(shí)間：2026年1月5日（周一）16:00-17:00
報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304報(bào)告廳
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
宋仁明，美國(guó)Illinois大學(xué)教授，1986年河北大學(xué)碩士畢業(yè)，1989年美國(guó)Florida大學(xué)博士畢業(yè)。訪(fǎng)問(wèn)過(guò)德國(guó)、法國(guó)、日本、韓國(guó)等國(guó)家和臺(tái)灣地區(qū)的20余所大學(xué)和研究所。從事隨機(jī)過(guò)程和隨機(jī)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(shù)學(xué)、概率國(guó)際權(quán)威刊物上發(fā)表論文160余篇；多次在國(guó)際學(xué)術(shù)會(huì)議上作邀請(qǐng)報(bào)告。
報(bào)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.