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DEFINITENESS OF THE PEANO KERNEL ASSOCIATED WITH THE POLYHARMONIC MEAN VALUE PROPERTY

Published online by Cambridge University Press:  30 October 2000

WERNER HAUßMANN  and
OGNYAN KOUNCHEV
WERNER HAUßMANN
Affiliation:
Department of Mathematics, Gerhard-Mercator-University, Duisburg, 47048 Duisburg, Germany Institute of Mathematics, Bulgarian Academy of Sciences, 8 Acad. G Bontchev Str., 1113 Sofia, Bulgaria
OGNYAN KOUNCHEV
Affiliation:
Department of Mathematics, Gerhard-Mercator-University, Duisburg, 47048 Duisburg, Germany Institute of Mathematics, Bulgarian Academy of Sciences, 8 Acad. G Bontchev Str., 1113 Sofia, Bulgaria
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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
Journal of the London Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 149 - 160
Copyright
The London Mathematical Society 2000

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