Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

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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