Derivatives of functions on the sierpinski gasket

Abstract

Let ƒ be a real-valued harmonic function on the Sierpinski gasket(SG) with bound-ary points p0,p1 and pg. We define three derivatives (three directions) at each junction point p in SG depending on its location. We will show that any harmonic function has finite derivatives at each junction point and obtain derivative formulas and some of their properties. Finally, we define another derivative on the set of junction points for which the first derivative coincides with the old definition for harmonic functions and the second derivative is zero at junction points.