ON THE P-HARMONIC RADII OF CIRCULAR SECTORS

被引：0
|
作者：
Afanaseva-Grigoreva, A. S. [1 ]
Prilepkina, E. G. [1 ,2 ]
机构：
[1] Far Eastern Fed Univ, Far Eastern Ctr Res & Educ Math, 10 Ajax Bay, Vladivostok 690922, Russia
[2] FEBRAS, Inst Appl Math, 7 Radio St, Vladivostok 690041, Russia
来源：
PROBLEMY ANALIZA-ISSUES OF ANALYSIS | 2021年 / 10卷 / 03期
关键词：
condenser capacities; conformal radius; harmonic radius; family of curves; CAPACITY;
D O I：
10.15393/j3.art.2021.10950
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：3 / 14
页数：12
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