报告人：顾庆松（南京大学）

时间：2023年12月30日 14:30-

地址：理科楼LA103

摘要：We study the boundary value problems for harmonic functions on open connected subsets of post-critically finite (p.c.f.) self-similar sets, on which the Laplacian is defined through a self-similar local regular Dirichlet form. For a p.c.f. self-similar set K, we prove that for any open connected subset Ω ⊂ K whose “geometric” boundary is a graph-directed self-similar set, there exists a finite number of matrices called flux transfer matrices whose products generate the hitting probability from a point in Ω to the “resistance” boundary ∂Ω. The harmonic functions on Ω can be expressed by integrating functions on ∂Ω against the probability measures. Furthermore, we obtain a two-sided estimate of the energy of a harmonic function in terms of its values on ∂Ω. This generalizes the known results on Sierpinski gasket to p.c.f. self-similar sets. The talk is based on a joint work with Hua Qiu.

简介：顾庆松助理研究员本科毕业于南京大学匡亚明学院，获理学学士学位，博士毕业于清华大学数学科学系，先后在香港中文大学与加拿大纽芬兰纪念大学做博士后，2020年9月至今在南京大学数学系工作。他的主要研究兴趣是分形上的分析，在分形上的Besov空间临界指数和狄氏型以及p-能量存在性等问题上取得了一些进展，相关成果发表在《Adv.Math.》、《J. Funct.Anal.》、《Trans.Amer.Math.Soc.》等杂志。

邀请人：孔德荣   罗军

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