Comptes Rendus
Partial differential equations
Characterization of balls via solutions of the modified Helmholtz equation
Nikolay Kuznetsov1
1 Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol’shoy pr. 61, St Petersburg 199178, Russian Federation
Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 945-948.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.250

Nikolay Kuznetsov 1

1 Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol’shoy pr. 61, St Petersburg 199178, Russian Federation
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Nikolay Kuznetsov. Characterization of balls via solutions of the modified Helmholtz equation. Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 945-948. doi : 10.5802/crmath.250. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.250/

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