题目:Boundary Harnack principle for non-local operators

报告人：陈振庆 教授

时间：12月25日 15：00-16：00

地点：西大楼108报告厅

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.

报告人简介：陈振庆 美国华盛顿大学（西雅图）数学系终身教授，分别于2007年和2014年当选为国际数理统计学会会士和美国数学学会会士，2019年荣获伊藤奖(Itô Prize)。主要从事概率论及随机过程的研究，现（曾）担任国际期刊Potential Analysis的主编以及AOP、AAP、SPA、EJP、JTP、PAMS等期刊编委。出版专著一部，在JEMS、MAMS、Math. Ann.、Adv. Math.、CMP、AOP、PTRF、TAMS、JFA等期刊发表论文一百九十余篇。

邀请人：宋玉林 老师