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) identifier identifier

  • 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.