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Comptes Rendus Mathematique
Article . 2021 . Peer-reviewed
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Comptes Rendus Mathematique
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Comptes Rendus Mathématique
Article . 2021
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https://dx.doi.org/10.5802/crm...
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Characterization of balls via solutions of the modified Helmholtz equation

descriptionPublicationkeyboard_double_arrow_right Article 06 Oct 2021 English Publisher:MathDoc/Centre MersenneJournal:Comptes Rendus. Mathématique, volume 359, pages 945-948 (issn: 1631-073X, eissn: 1778-3569, Copyright policy )
Authors: Kuznetsov, Nikolay;

doi: 10.5802/crmath.250

Characterization of balls via solutions of the modified Helmholtz equation

Abstract

A theorem characterizing analytically balls in the Euclidean space ℝ m is proved. For this purpose positive solutions of the modified Helmholtz equation are used instead of harmonic functions applied in previous results. The obtained Kuran type theorem is based on the volume mean value property of solutions to this equation.

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Keywords

Second-order elliptic equations, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, QA1-939, Mathematics, characterization of balls, modified Helmholtz equation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Average
Top 10%
gold