TITLE:
Hölder Derivative of Harmonic Functions on Sierpinski Gasket
AUTHORS:
Guangjun Yang, Ping Wang
KEYWORDS:
Holder Derivative, Harmonic Function, Sierpinski Gasket
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.2,
February
19,
2025
ABSTRACT: In the past years, we established analytic expressions of various fractals and discussed Hölder derivatives of the expressions. Based on our earlier results, we will study the properties of harmonic functions on a very important fractal, the Sierpinski gasket (SG). Our main result is that the harmonic function on SG satisfies a Hölder inequality of order
α=ln
3
5
\ln2
.