Properties of Harmonic Functions on Koch Curve
Abstract
Recently, we discussed the properties of harmonic functions on the Sierpinski gasket (SG) and proved the Holder derivative of the harmonic functions. In this paper, based on the quaternary expressions of the Koch curve, another very important fractal, we will construct harmonic functions on the fractal and discuss some properties of the derivative of the harmonic functions. The main result is that first quaternary derivative is found to be constant.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Analytic and geometric function theory
Publication details
- Journal / source
- Journal of Applied Mathematics and Physics
- Volume
- 14
- Issue
- 02
- Pages
- 559–565
- Publication date
- 1 January 2026