学术报告

【online】分形分析系列报告(二):Resistance estimates and Dirichlet forms on some classes of non-p.c.f. fractals

发布人:发布时间: 2020-06-03

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分形分析系列报告(二)

题目:Resistance estimates and Dirichlet forms on some classes of non-p.c.f. fractals

 

报告人:顾庆松清华大学博士

 

报告时间2020619日(周五) 21:40-22:40

 

摘要:The resistance estimate of network approximation is an important tool to study analytic properties of fractals such as  Laplacians, spectral dimensions, walk dimensions.  I will talk about the resistance growth rates on two new classes of fractals; they are constructed by dividing a unit triangle into sub-triangles, then removing some of them in a symmetric pattern. One class we call it triangular carpets is analogous to the Sierpinski carpet. The other class we call it triangular diamonds is graph directed finitely ramified, and is a generalization of the diamond fractal. After verifying the resistance growth rates, we use them to derive a uniform Harnack inequality on the approximation networks. Then apply them to study the $\Gamma$-convergence of the associated Besov spaces to obtain the existence of a local regular Dirichlet form on the fractals, a recent approach to obtain a Laplacian initiated by Grigor'yan and Yang.

 

报告方式:Zoom会议 ID5036881879; 地址:https://zoom.com.cn/j/5036881879

 

邀请人:邱华 老师