Extremal decomposition problems for p-harmonic radius

Abstract

We extend classical results by Lavrent'ev and Kufarev concerning the product of the conformal radii of planar non-overlapping domains. We also extend relatively recent results for the case of domains in the $n$-dimensional Euclidean space, $n\ge 3$, with conformal radii replaced by harmonic ones. Namely, we get analogues of these results in $n$-dimensional Euclidean space in terms of $p$-harmonic radius. The proofs are based on technique of modulii of curve families and dissymmetrization of such families.

15 pages, 4 figures