LOCAL AND NON-LOCAL DIRICHLET FORMS ON THE SIERPITSKI CARPET

被引：10

作者：

Grigor'yan, Alexander ^{[1
]}

Yang, Meng ^{[1
,2
]}

机构：

[1] Univ Bielefeld, Fak Math, Postfach 100131, D-33501 Bielefeld, Germany

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 06期

关键词：

Sierpinski carpet; non-local quadratic form; walk dimension; Gamma-convergence; Brownian motion; effective resistance; heat kernel; HEAT KERNELS; BROWNIAN-MOTION; DIFFUSION-PROCESSES; HARMONIC-ANALYSIS; RESISTANCE; FRACTALS;

D O I：

10.1090/tran/7753

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpinski carpet using approximation of stable-like non-local closed forms which gives an answer to an open problem in analysis on fractals.

引用

页码：3985 / 4030

页数：46

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