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Weighted Means and Characterization of Balls

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Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities, some applications of which are presented. Also, new analytic characterizations of balls are proved; each of them requires the volume mean of a single weight function over the domain under consideration to be equal to a prescribed number depending on the weight.

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Authors and Affiliations

  1. Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, RAS, V.O., Bol’shoy pr. 61, St Petersburg, 199178, Russia

    N. Kuznetsov

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  1. N. Kuznetsov
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Correspondence to N. Kuznetsov.

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JMS Source Journal International Mathematical Schools. Vol. 2. Advances in Pure and Applied Mathematics

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Kuznetsov, N. Weighted Means and Characterization of Balls. J Math Sci 269, 853–858 (2023). https://doi.org/10.1007/s10958-023-06323-2

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  • DOI: https://doi.org/10.1007/s10958-023-06323-2

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