A generalization of the Liouville theorem to polyharmonic functions

Toshihide FUTAMURA; Kyoko KISHI; Yoshihiro MIZUTA

doi:10.2969/jmsj/05310113

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

A generalization of the Liouville theorem to polyharmonic functions

Toshihide FUTAMURA, Kyoko KISHI, Yoshihiro MIZUTA

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Keywords: polyharmonic functions, Almansi expansion, Green's formula, mean value property

JOURNAL FREE ACCESS

2001 Volume 53 Issue 1 Pages 113-118

DOI https://doi.org/10.2969/jmsj/05310113

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Abstract

The aim of this note is to generalize the Liouville theorem to poly-harmonic functions u on \bm{R}ⁿ. We give a condition on spherical means to assure that u is a polynomial.

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