On the box dimension of graph of harmonic functions on the Sierpiński gasket

Abstract

In this paper, we have obtained bounds for the box dimension of graph of harmonic function on the Sierpiński gasket. Also we get upper and lower bounds for the box dimension of graph of functions that belongs to $\text{dom}(\mathcal{E}),$ that is, all finite energy functionals on the Sierpiński gasket. Further, we show the existence of fractal functions in the function space $\text{dom}(\mathcal{E})$ with the help of fractal interpolation functions. Moreover, we provide bounds for the box dimension of some functions that belong to the family of continuous functions and arise as fractal interpolation functions.

17 pages, 1 figure