Year: 2014
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 3 : pp. 296–305
Abstract
In this paper we establish sharp Hölder 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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2014.v30.n3.6
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 3 : pp. 296–305
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: p.c.f. self-similar sets Hölder estimates harmonic function.
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