Harmonic functions on the Sierpinski triangle
arXiv:1205.4442
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 Hölder 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.
24 pages, 7 figures