## Hiroshima Mathematical Journal

### A generalization of Bôcher's theorem for polyharmonic functions

#### Abstract

In this paper we generalize Bôcher's theorem for polyharmonic functions $u$. In fact, if $u$ is polyharmonic outside the origin and satisfies a certain integral condition, then it is shown that $u$ is written as the sum of partial derivatives of the fundamental solution and a polyharmonic function near the origin.

#### Article information

Source
Hiroshima Math. J., Volume 31, Number 1 (2001), 59-70.

Dates
First available in Project Euclid: 28 June 2006

https://projecteuclid.org/euclid.hmj/1151511148

Digital Object Identifier
doi:10.32917/hmj/1151511148

Mathematical Reviews number (MathSciNet)
MR1820695

Zentralblatt MATH identifier
1013.31005

Subjects
Primary: 31B30: Biharmonic and polyharmonic equations and functions

#### Citation

Futamura, Toshihide; Kishi, Kyoko; Mizuta, Yoshihiro. A generalization of Bôcher's theorem for polyharmonic functions. Hiroshima Math. J. 31 (2001), no. 1, 59--70. doi:10.32917/hmj/1151511148. https://projecteuclid.org/euclid.hmj/1151511148