Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet

被引：11

作者：

Hambly, B. M. ^{[1
]}

机构：

[1] Univ Oxford, Math Inst, Oxford, England

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2011年 / 63卷 / 01期

关键词：

AFFINE NESTED FRACTALS; VON-KOCH SNOWFLAKE; SELF-SIMILAR SETS; BROWNIAN-MOTION; TRANSITION DENSITIES; SPECTRAL ASYMPTOTICS; EQUATION; LAPLACIANS; RESISTANCE; BOUNDARY;

D O I：

10.4153/CJM-2010-079-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the asymptotic behaviour of the partition function, the heat content, the integrated eigenvalue counting function, and, for certain points, the on-diagonal heat kernel of generalized Sierpinski carpets. For all these functions the leading term is of the form x(gamma)phi(log x) for a suitable exponent gamma and phi a periodic function. We also discuss similar results for the heat content of affine nested fractals.

引用

页码：153 / 180

页数：28

共 28 条

[1]

[Anonymous], 1998, Lecture notes Math

[2]

[Anonymous], 2001, ANAL FRACTALS

[3] Uniqueness of Brownian motion on Sierpinski carpets [J].