長(zhǎng)沙理工大學(xué)學(xué)術(shù)活動(dòng)預(yù)告
報(bào)告承辦單位:數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(nèi)容: Potential Theory of Subordinate Brownian Motions
報(bào)告人姓名:宋仁明
報(bào)告人所在單位:美國(guó) Illinois大學(xué)數(shù)學(xué)系
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜:教授，博導(dǎo)
報(bào)告時(shí)間:8月1日16:00 – 17:00
報(bào)告地點(diǎn):理科樓410
報(bào)告人簡(jiǎn)介：宋仁明, 教授, 1983和1986年畢業(yè)于河北大學(xué)數(shù)學(xué)系，獲得理學(xué)學(xué)士和碩士學(xué)位; 1993年畢業(yè)于佛羅里達(dá)大學(xué)數(shù)學(xué)系，獲得哲學(xué)博士學(xué)位。1994年到密西根大學(xué)數(shù)學(xué)系任教，此后分別于1997、2003、2009獲得伊利諾斯大學(xué)數(shù)學(xué)系助理教授、副教授和教授職位。宋仁明教授主要從事隨機(jī)分析和Markov過程研究，任國(guó)際期刊《Journal of Korean Mathematical Society》編輯、《llinois Journal of Mathematics》主編，已發(fā)表學(xué)術(shù)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.
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