Energy and Laplacian on the Sierpinski gasket

被引：0

作者：

Teplyaev, A ^{[1
]}

机构：

[1] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

来源：

FRACTAL GEOMETRY AND APPLICATIONS: A JUBILEE OF BENOIT MANDELBROT - ANALYSIS, NUMBER THEORY, AND DYNAMICAL SYSTEMS, PT 1 | 2004年 / 72卷

关键词：

Sierpifiski gasket; fractal; self-similar; Dirichlet form; Laplacian; partition of energy; energy measure; Apollonian packing; harmonic coordinates; resistance networks;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This is an expository paper which includes several topics related to the Dirichlet form analysis on the Sierpinski gasket. We discuss the analog of the classical Laplacian; approximation by harmonic functions that gives a notion of a gradient; directional energies and an equipartition of energy; analysis with respect to the energy measure; harmonic coordinates; and non self-similar Dirichlet forms on the Sierpinski gasket, one of which is defined by the Apollonian packing.

引用

页码：131 / 154

页数：24

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