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Boundary value problems for harmonic functions on domains in p.c.f. self-similar sets

发布日期:2023-12-25点击数:

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,20209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。


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