Derivatives of the restrictions of harmonic functions on the Sierpinski gasket to segments
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.333, sa.2, ss.817-822, 2007 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 333 Sayı: 2
- Basım Tarihi: 2007
- Doi Numarası: 10.1016/j.jmaa.2006.11.025
- Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.817-822
- Anahtar Kelimeler: analysis on fractals, Sierpinski gasket, harmonic functions
- Anadolu Üniversitesi Adresli: Evet
Özet
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.