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Oscillation And Dimensions Of Harmonic Functions On The Sierpiåƒski Gaskets

Author

Listed:
  • ZHEN LIANG

    (School of Mathematics, Nanjing Audit University, Nanjing 211815, P. R. China)

  • HUO-JUN RUAN

    (School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, P. R. China)

Abstract

In this paper, we estimate the oscillation of harmonic functions on the (N − 1)-dimensional Sierpiński gasket KN, where K3 is the classical Sierpiński gasket. By using this result, we prove that both the box dimension and the Hausdorff dimension of graphs of harmonic functions on KN are log2N.

Suggested Citation

  • Zhen Liang & Huo-Jun Ruan, 2025. "Oscillation And Dimensions Of Harmonic Functions On The Sierpiåƒski Gaskets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-6.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:03:n:s0218348x24501342
    DOI: 10.1142/S0218348X24501342
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