Geodesic
On mean value properties involving a logarithm-type weight
Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 419-425
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Two new assertions characterizing analytically disks in the Euclidean plane $\mathbb {R}^2$ are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier.
Two new assertions characterizing analytically disks in the Euclidean plane $\mathbb {R}^2$ are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier.
DOI : 10.21136/MB.2023.0072-23
Classification : 31A10, 35B05, 35J05
Keywords: harmonic function; Helmholtz equation; modified Helmholtz equation; mean value property; logarithmic weight; characterization of balls 
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Kuznetsov, Nikolay. On mean value properties involving a logarithm-type weight. Mathematica Bohemica, Tome 149 (2024) no. 3, pp. 419-425. doi: 10.21136/MB.2023.0072-23

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