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On the mean value property for polyharmonic functions

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Abstract

We derive differential relations between spherical and solid means of continuous functions. Next we use the relations to give inductive proofs of the mean value property for polyharmonic functions and its converse in arbitrary dimension.

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland

    Grzegorz Łysik

  2. Jan Kochanowski University, Kielce, Poland

    Grzegorz Łysik

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  1. Grzegorz Łysik
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Correspondence to Grzegorz Łysik.

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Łysik, G. On the mean value property for polyharmonic functions. Acta Math Hung 133, 133–139 (2011). https://doi.org/10.1007/s10474-011-0138-7

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  • DOI: https://doi.org/10.1007/s10474-011-0138-7

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