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H?lder Derivative of Harmonic Functions on Sierpinski Gasket

DOI: 10.4236/jamp.2025.132025, PP. 465-474

Keywords: Holder Derivative, Harmonic Function, Sierpinski Gasket

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Abstract:

In the past years, we established analytic expressions of various fractals and discussed H?lder 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 H?lder inequality of order α=ln 3 5 \ln2 .

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