Peano kernel associated with the polyharmonic mean value property in the annulus |
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| Authors: | Werner Haußmann Ognyan Kounchev |
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| Institution: | 1. Department of Mathematics , Gerhard-Mercator-University , Duisburg, 47048, Germany;2. Department of Mathematics , Bulgarian Academy of Sciences , Acad. G. Bonchev Str. 8, Sofia, 1118, Bulgaria |
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| Abstract: | The well known mean value property for polyharmonic functions in the ball (see Picone 9], Bramble-Payne 2]) is generalized to the case of an annular domain. We prove that the Peano kernel arising from this new mean value property has definite sign. It is a polyspline in the sense of 8]. The present results generalize former investigations concerning the Peano kernel associated with the mean value property of polyharmonic functions in the ball. |
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