%0 Journal Article
%T Hölder Derivative of Harmonic Functions on Sierpinski Gasket
%A Guangjun Yang
%A Ping Wang
%J Journal of Applied Mathematics and Physics
%P 465-474
%@ 2327-4379
%D 2025
%I Scientific Research Publishing
%R 10.4236/jamp.2025.132025
%X In the past years, we established analytic expressions of various fractals and discussed H&#246;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&#246;lder inequality of order <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>&#x03B1;</mi><mo>=</mo><mi>ln</mi><mfrac>
   <mn>3</mn>
   <mn>5</mn>
  </mfrac>
  <mo>&#x005C;</mo><mi>ln</mi><mn>2</mn></mrow>
</math>

.
%K Holder Derivative
%K Harmonic Function
%K Sierpinski Gasket
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=140656