A generalized mean value property for polyharmonic functions

作     者：Floater, Michael S. 

作者机构：Univ Oslo Dept Math Moltke Moes Vei 35 N-0851 Oslo Norway 

出 版 物：《NUMERICAL ALGORITHMS》 (数值算法)

年 卷 期：2016年第73卷第1期

页      面：157-165页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Polyharmonic functions Polynomial interpolation Integral formulas 

摘      要：A well known property of a harmonic function in a ball is that its value at the centre equals the mean of its values on the boundary. Less well known is the more general property that its value at any point x equals the mean over all chords through x of its values at the ends of the chord, linearly interpolated at x. In this paper we show that a similar property holds for polyharmonic functions of any order when linear interpolation is replaced by two-point Hermite interpolation of odd degree.