Derivatives of the restrictions of harmonic functions on the Sierpinski gasket to segments |
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Authors: | Bü nyamin Demir,Vakif Dzhafarov,?ahin Koç ak,Mehmet Ü reyen |
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Affiliation: | Anadolu University, Mathematics Department, 26470 Eski?ehir, Turkey |
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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. |
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Keywords: | Analysis on fractals Sierpinski gasket Harmonic functions |
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