H ¨older Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

Donglei Tang,Rui Hu 已出版文章查询
Donglei Tang,Rui Hu
1 Chunwei Pan 已出版文章查询
Chunwei Pan

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1Department of Applied Mathematics, Nanjing Audit University, Nanjing 210029, China

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In this paper we establish sharp H ¨older estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some well-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.

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DOI: http://dx.doi.org/10.4208/ata.2014.v30.n3.6

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