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The Laplacian on p.c.f. self-similar sets via the method of averages

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  • Tang, Donglei

Abstract

We show how the symmetric Laplacian on p.c.f. self-similar sets, together with its associated Dirichlet form and harmonic functions, can be defined entirely in terms of average values of a function over basic sets. The approach combined the constructive limit-of-difference-quotients method of Kigami and the method of averages introduced by Kusuoka and Zhou for the Sierpinski carpet. We consider well-known examples, such as the unit interval, the Vicsek set,the hexagasket, and SG4. This paper has generalized the results in [11,13,14], but a different proof is needed.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:7:p:538-547
    DOI: 10.1016/j.chaos.2011.05.003
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    References listed on IDEAS

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    1. 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.
    2. 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. Ri, SongIl, 2020. "Fractal functions on the Sierpinski Gasket," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

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