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

Demir, BÜNYAMİN; Dzhafarov, Vakif; Kocak, Sahin; Ureyen, Mehmet

doi:10.1016/j.jmaa.2006.11.025

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

Demir B., Dzhafarov V., Kocak S., Ureyen M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.333, no.2, pp.817-822, 2007 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 333 Issue: 2
Publication Date: 2007
Doi Number: 10.1016/j.jmaa.2006.11.025
Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.817-822
Keywords: analysis on fractals, Sierpinski gasket, harmonic functions
Anadolu University Affiliated: Yes

Abstract

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.