Mean value properties of harmonic functions on Sierpinski gasket type fractals

2012/06/07 by Hua Qiu, Robert S. Strichartz, Qiu, Hua +1
Mathematics · Physics and Astronomy · #28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #advanced mathematical theories #math.CA #msc:28A80

paper · pdf · doi:10.48550/arxiv.1206.1382

27 pages, 9 figures, to appear, JFAA

openalex publication_date 2012/06/07 · arxiv created 2013/05/16 · arxiv updated 2013/05/17 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Furthermore, we extend the result to some other p.c.f. fractals with Dihedral-3 symmetry.

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