ON THE P-HARMONIC RADII OF CIRCULAR SECTORS
It is proved that the property of logarithmic concavity of the conformal radius of a circular sector (considered as a function of the angle) extends to the domains of Euclidean space. In this case, the conformal radius is replaced by 𝑝-harmonic one, and the fundamental solution of the Laplace 𝑝-equa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2021-11-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10950&lang=ru |
| Summary: | It is proved that the property of logarithmic concavity of the conformal radius of a circular sector (considered as a function of the angle) extends to the domains of Euclidean space. In this case, the conformal radius is replaced by 𝑝-harmonic one, and the fundamental solution of the Laplace 𝑝-equation acts as logarithm. In the case of 𝑝 = 2, the presence of an asymptotic formula for the capacity of a degenerate condenser allows us to generalize this result to the case of a finite set of points. The method of the proof leads to the solution of one particular case of an open problem of A. Yu. Solynin. |
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| ISSN: | 2306-3424 2306-3432 |