报告题目：The weak and strong elliptic Harnack inequalities
时 间：2024年1月24日（星期三）14：30
地 点：理工北楼601
主 办：数学与统计学院，分析数学及应用教育部重点实验室，福建省应用数学中心（福建师范大学），福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：In this talk, we consider the regular resurrected Dirichlet form on the metric space equipped with a doubling measure. We show that the heat kernel estimate is equivalent to the weak elliptic Harnack inequality, the mean exit time estimate, plus the jump kernel upper bound. If further the upper jumping smoothness holds, we obtain a sharper assertion, that is, the strong elliptic Harnack inequality also comes into the stage. In particular, for the strongly local Dirichlet form where the jump vanishes (so that both the jump kernel upper bound and the upper jumping smoothness are trivially satisfied), our assertion coincides with the one achieved by Grigor'yan, Hu and Lau (2015 JMS Japan). This talk is based on the joint work with Zhenyu Yu.
报告人简介： 胡家信，清华大学数学科学系长聘教授、博士生导师。长期从事偏微分方程、调和分析、分形几何、狄氏型理论与热核估计等相关领域的研究，主要成果发表于Invent. Math.,Comm. Pure Appl. Math.,Comm. Math. Phys., Adv. Math.等著名学术期刊，曾获德国洪堡高级访问学者荣誉，主持多项国家自然科学基金。