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arXiv · 1205.4442

Harmonic functions on the Sierpinski triangle

Ilia Smilga
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Abstract

In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle - more precisely, of their restriction to a side of the triangle. First we present a general formula that gives the H\"older exponent of such a function in a given point. From this formula, we deduce an explicit algorithm to calculate this exponent in any rational point, and the fact that the derivative of such a function is always equal to 0, infinity or undefined.

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Ilia Smilga. 2012-05-20. Harmonic functions on the Sierpinski triangle. https://arxiv.org/abs/1205.4442

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