报告人：陈振庆(美国华盛顿大学)

时间：2024年06月19日 08：30

地址: 理科楼 LA103

摘要：The classical boundary Harnack principle asserts that two positive harmonic functions that vanish on a portion of the boundary of a smooth domain decay at the same rate. It is well known that scale invariant boundary Harnack inequality holds for Laplacian \Delta on uniform domains and holds for fractional Laplacians \Delta^s on any open sets. It has been an open problem whether the scale-invariant boundary Harnack inequality holds on bounded Lipschitz domains for Levy processes with Gaussian components such as the independent sum of a Brownian motion and an isotropic stable process (which corresponds to \Delta + \Delta^s).

In this talk, I will present a necessary and sufficient condition for the scale-invariant boundary Harnack inequality to hold for a class of non-local operators on metric measure spaces through a probabilistic consideration. This result will then be applied to give a sufficient geometric condition for the scale-invariant boundary Harnack inequality to hold for subordinate Brownian motions having Gaussian components on bounded Lipschitz domains in Euclidean spaces. This condition is almost optimal and a counterexample will be given showing that the scale-invariant BHP may fail on some bounded Lipschitz domains with large Lipschitz constants.

Based on joint work with Jieming Wang.

简介：陈振庆教授是国际知名概率论学者。美国华盛顿大学（西雅图）数学系教授，1992年在美国华盛顿大学（圣路易斯）获博士学位，曾在美国的加利福尼亚大学（圣地亚哥）和康奈尔大学工作；1998年起在位于华盛顿州西雅图市的华盛顿大学数学系工作至今。在包括国际顶尖数学和概率期刊《欧洲数学学会杂志》(Journal of the European Mathematical Society)、《概率年刊》(Annals of Probability)、《概率论及其相关领域》(Probabiity Theory and Related Fields)等学术期上发表论文200余篇，著有两本专著。被列为全球Top 2%顶尖科学家。陈振庆教授是国际数理统计学会会士和美国数学学会会士。 从2016年起任国际数学综合性期刊《位势理论》的主编,是《美国数学学会通讯》(Proceedings ofthe American Mathematical Society)应用数学和概率统计方向的协调编辑(Coordinating ditor) 及多个国际数学和概率期刊的编委。

邀请人：周国立