no. 8
Équations aux dérivées partielles
Characterization of balls via solutions of the modified Helmholtz equation
Kuznetsov, Nikolay1
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, Tome 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.

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DOI : 10.5802/crmath.250
Kuznetsov, Nikolay 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 
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Kuznetsov, Nikolay. Characterization of balls via solutions of the modified Helmholtz equation. Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 945-948. doi : 10.5802/crmath.250. http://www.numdam.org/articles/10.5802/crmath.250/

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