Derivatives of the restrictions of harmonic functions on the Sierpinski gasket to segments

被引：4

作者：

Demir, Bunyamin ^{[1
]}

Dzhafarov, Vakif ^{[1
]}

Kocak, Sahin ^{[1
]}

Ureyen, Mehmet ^{[1
]}

机构：

[1] Anadolu Univ, Dept Math, TR-26470 Eskisehir, Turkey

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 333卷 / 02期

关键词：

analysis on fractals; Sierpinski gasket; harmonic functions;

D O I：

10.1016/j.jmaa.2006.11.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give an explicit derivative computation for the restriction of a harmonic function on SG to segments at specific points of the segments: The derivative is zero at points dividing the segment in ratio 1:3. This shows that the restriction of a harmonic function to a segment of SG has the following curious property: The restriction has infinite derivatives on a dense subset of the segment (at junction points) and vanishing derivatives on another dense subset. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：817 / 822

页数：6