長沙理工大學學術活動預告
報告承辦單位:數學與統計學院
報告內容: Potential Theory of Subordinate Brownian Motions
報告人姓名:宋仁明
報告人所在單位:美國 Illinois大學數學系
報告人職稱/職務及學術頭銜:教授，博導
報告時間:8月1日16:00 – 17:00
報告地點:理科樓410
報告人簡介：宋仁明, 教授, 1983和1986年畢業于河北大學數學系，獲得理學學士和碩士學位; 1993年畢業于佛羅里達大學數學系，獲得哲學博士學位。1994年到密西根大學數學系任教，此后分別于1997、2003、2009獲得伊利諾斯大學數學系助理教授、副教授和教授職位。宋仁明教授主要從事隨機分析和Markov過程研究，任國際期刊《Journal of Korean Mathematical Society》編輯、《llinois Journal of Mathematics》主編，已發表學術論文百余篇。
摘要: A subordinate Brownian motion can be obtained by replacing the time parameter of a Brownian motion by an independent increasing Levy process (i.e., a subordinator). Subordinate Brownian
Motions form a large subclass of Levy processes and they are very important in various applications. The generator of a subordinate Brownian motion is a function of the Laplacian. In this talk, I will give a survey of some of the recent results in the study of the potential theory of the subordinate Brownian motions. In particular, I will present recent results on sharp two-sided estimates on the transition densities of killed subordinate Brownian motion in smooth open sets, or equivalently, sharp two-sided estimates on the Dirichlet heat kernels of the generators of the subordinate Brownian motion.