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 |
| _version_ | 1811335785188687872 |
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| author | A. S. Afanaseva-Grigoreva E. G. Prilepkina |
| author_facet | A. S. Afanaseva-Grigoreva E. G. Prilepkina |
| author_sort | A. S. Afanaseva-Grigoreva |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T17:29:14Z |
| format | Article |
| id | doaj.art-fd2c199f278d41908eb6df2fe69f3590 |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-04-13T17:29:14Z |
| publishDate | 2021-11-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-fd2c199f278d41908eb6df2fe69f35902022-12-22T02:37:38ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322021-11-0110(28)331410.15393/j3.art.2021.10950ON THE P-HARMONIC RADII OF CIRCULAR SECTORSA. S. Afanaseva-Grigoreva0E. G. Prilepkina1Far Eastern Federal University, Far Eastern Center for Research and Education in Mathematics 10 Ajax Bay, Russky Island, Vladivostok 690922, RussiaFar Eastern Federal University, Far Eastern Center for Research and Education in Mathematics 10 Ajax Bay, Russky Island, Vladivostok 690922, Russia ; Institute of Applied Mathematics, FEBRAS 7 Radio Street, Vladivostok 690041, RussiaIt 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.https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10950&lang=rucondenser capacitiesconformal radiusfamily of curvesharmonic radius |
| spellingShingle | A. S. Afanaseva-Grigoreva E. G. Prilepkina ON THE P-HARMONIC RADII OF CIRCULAR SECTORS Проблемы анализа condenser capacities conformal radius family of curves harmonic radius |
| title | ON THE P-HARMONIC RADII OF CIRCULAR SECTORS |
| title_full | ON THE P-HARMONIC RADII OF CIRCULAR SECTORS |
| title_fullStr | ON THE P-HARMONIC RADII OF CIRCULAR SECTORS |
| title_full_unstemmed | ON THE P-HARMONIC RADII OF CIRCULAR SECTORS |
| title_short | ON THE P-HARMONIC RADII OF CIRCULAR SECTORS |
| title_sort | on the p harmonic radii of circular sectors |
| topic | condenser capacities conformal radius family of curves harmonic radius |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10950&lang=ru |
| work_keys_str_mv | AT asafanasevagrigoreva onthepharmonicradiiofcircularsectors AT egprilepkina onthepharmonicradiiofcircularsectors |