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Mathematics > Analysis of PDEs

arXiv:2210.00879 (math)
[Submitted on 26 Sep 2022 (v1), last revised 12 Feb 2023 (this version, v4)]

Title:Weighted means of harmonic functions and characterization of balls

Authors:Nikolay Kuznetsov
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Abstract:Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities 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.
Comments: 7 pages, no figures
Subjects: Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA)
Cite as: arXiv:2210.00879 [math.AP]
  (or arXiv:2210.00879v4 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2210.00879

Submission history

From: Nikolay Kuznetsov G. [view email]
[v1] Mon, 26 Sep 2022 15:50:31 UTC (4 KB)
[v2] Wed, 5 Oct 2022 10:54:06 UTC (4 KB)
[v3] Tue, 1 Nov 2022 11:38:12 UTC (5 KB)
[v4] Sun, 12 Feb 2023 16:39:37 UTC (6 KB)
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