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The Laplacian on β-sets via the method of averages

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  • Donglei, Tang
  • Weiyi, Su

Abstract

In this paper, we show how the symmetric Laplacian on β-sets with 0<β<12, together with its associated Dirichlet form and harmonic functions, can be defined entirely in terms of average values of a function over basic sets. We have generalized Strichartz’s and our previous results by using the method of averages.

Suggested Citation

  • Donglei, Tang & Weiyi, Su, 2007. "The Laplacian on β-sets via the method of averages," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 147-154.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:147-154
    DOI: 10.1016/j.chaos.2005.09.041
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    1. Donglei, Tang & Weiyi, SU, 2005. "The Laplacian on the level 3 Sierpinski gasket via the method of averages," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1201-1209.
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    Cited by:

    1. Tang, Donglei, 2011. "The Laplacian on p.c.f. self-similar sets via the method of averages," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 538-547.

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