The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets

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Abstract

In this paper we establish the oscillation inequality of harmonic functions and Hölder estimate of the functions in the domain of the Laplacian on connected post critically finite (p.c.f.) self-similar sets.

Keywords:

p.c.f. Self-similar sets oscillation inequality Hölder estimate harmonic functions.
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DOI

10.4208/ata.2017.v33.n2.5

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The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets. (2017). Analysis in Theory and Applications, 33(2), 149-156. https://doi.org/10.4208/ata.2017.v33.n2.5