Potential theory of Markov processes with
jump kernels blowing up at the boundary
报告专家：Renming Song（UIUC）
报告时间：5月12日（星期二）下午3:00-5:00 ；5月15日（星期五）下午3:00-5:00
报告地点：四川大学数学学院西303
报告摘要：
In these talks, I will give a survey of some recent results about purely discontinuous symmetric Markov processes on subsets D of R^d with jump kernels of the form J(x,y)=|x-y|^{-d-\alpha}B(x,y),\alpha\in (0,2), where the function 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, 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. These talks are based on some recent joint works with Soobin Cho, Panki Kim and Zoran Vondracek.
专家简介：
宋仁明，美国伊利诺伊大学数学系教授，主要从事随机分析和马氏过程的研究。1979年考入河北大学数学系，1983年和1986年分别获得学士和硕士学位；1993年毕业于佛罗里达大学数学系，获博士学位；博士毕业后曾到美国西北大学、密西根大学工作，1997年进入伊利诺伊大学数学系。在马氏过程、位势理论、随机分析与分支过程等领域做出了众多杰出的成果，在数学和概率著名杂志上发表论文180篇，出版专著2部。
邀请人：胡泽春
