报 告 人：陈振庆 教授
报告题目：Boundary Harnack principle for diffusion processes with jumps
报告时间：2024年11月20日（星期三）下午3：30
报告地点：静远楼1506学术报告厅
主办单位：数学研究院、数学与统计学院、科学技术研究院
报告人简介：
陈振庆，美国华盛顿大学（西雅图）数学系教授，分别于2007年和2014年当选为美国数理统计学会士(Fellow)和美国数学学会会士(Fellow)。陈振庆教授主要从事概率论及随机过程的研究，主要的研究方向包括概率论以及随机分析，马尔可夫过程以及狄氏空间理论，随机微分方程，扩散过程，稳定过程以及偏微分方程中的概率方法等。发表学术论文200余篇，学术专著两部，国际期刊Potential Analysis的主编，2019年获伊藤奖 (Ito Prize)。
报告摘要：
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 diffusion processes with jumps on metric measure spaces. 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.