Extremal decomposition problems for p-harmonic Robin radius

A. S. Afanaseva-Grigoreva^a, E. G. Prilepkina<sup>b

a</sup> Far Eastern Federal University, Vladivostok
^b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok

Abstract: The theorems on the extremal decomposition of plane domains concerning to the products of Robin's radii are extended to the case of domains in Euclidean space. In some cases, the classical non-overlapping condition is weakened. The proofs are based on the moduli technique for families of curves and dissymmetrization.

Key words: p-harmonic radius, Robin radius, modulus of a family of curves, dissymmetrization, extremal decompositions.

UDC: 517.54

MSC: 31B99

Received: 28.07.2020

DOI: 10.47910/FEMJ202014