A generalization of the Liouville theorem to polyharmonic functions

Toshihide FUTAMURA; Kyoko KISHI; Yoshihiro MIZUTA

doi:10.2969/jmsj/05310113

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Home > Journals > J. Math. Soc. Japan > Volume 53 > Issue 1 > Article

January, 2001 A generalization of the Liouville theorem to polyharmonic functions

Toshihide FUTAMURA, Kyoko KISHI, Yoshihiro MIZUTA

J. Math. Soc. Japan 53(1): 113-118 (January, 2001). DOI: 10.2969/jmsj/05310113

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Abstract

The aim of this note is to generalize the Liouville theorem to polyharmonic functions $u$ on $R^{n}$ . We give a condition on spherical means to assure that $u$ is a polynomial.

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Toshihide FUTAMURA. Kyoko KISHI. Yoshihiro MIZUTA. "A generalization of the Liouville theorem to polyharmonic functions." J. Math. Soc. Japan 53 (1) 113 - 118, January, 2001. https://doi.org/10.2969/jmsj/05310113

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Published: January, 2001

First available in Project Euclid: 9 June 2008

zbMATH: 0977.31005

MathSciNet: MR1800525

Digital Object Identifier: 10.2969/jmsj/05310113

Subjects:

Primary: 31B30

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

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J. Math. Soc. Japan

Vol.53 • No. 1 • January, 2001

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Toshihide FUTAMURA, Kyoko KISHI, Yoshihiro MIZUTA "A generalization of the Liouville theorem to polyharmonic functions," Journal of the Mathematical Society of Japan, J. Math. Soc. Japan 53(1), 113-118, (January, 2001)

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