Article contents
DEFINITENESS OF THE PEANO KERNEL ASSOCIATED WITH THE POLYHARMONIC MEAN VALUE PROPERTY
Published online by Cambridge University Press: 30 October 2000
Abstract
The definiteness of the Peano kernel is proved for a functional associated with the mean-value property of Picone and Bramble and Payne for polyharmonic functions in the ball. An important corollary of this is that if a function f satisfying (−1)pΔpf>0 vanishes on p concentric spheres centered at 0, then f(0)>0. This generalizes a well-known property of subharmonic functions (which arise in the special case p = 1).
- Type
- Research Article
- Information
- Copyright
- The London Mathematical Society 2000
- 1
- Cited by