Mean Value Property of Harmonic Functions on the Tetrahedral Sierpinski Gasket

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Abstract

In this paper, we study the mean value property for both the harmonic functions and the functions in the domain of the Laplacian on the tetrahedral Sierpinski gasket. This paper is a continuation of the work of Strichartz and the first author (Qiu and Strichartz, J Fourier Anal Appl 19:943–966, 2013)where the same property on p.c.f. self-similar sets with Dihedral-3 symmetry was considered.

Keywords

Mean value property Tetrahedral Sierpinski gasket Harmonic functions Laplacian Self-similar sets 

Mathematics Subject Classification

Primary: 28A80 

Notes

Acknowledgements

The research of the Hua Qiu and Kui Yao were supported by the National Science Foundation of China, Grant 11471157.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China
  2. 2.Institute of SciencePLA University of Science and TechnologyNanjingPeople’s Republic of China

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