On the p-harmonic radii of circular sectors
A. S. Afanaseva-Grigoreva, E. G. Prilepkina · Problemy analiza · 2021
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.