ON the p-Harmonic Robin Radius in the Euclidean Space

Abstract

For p > 1, the notion of the p-harmonic Robin radius of a domain in the space ℝ n , n ≥ 2, is introduced. In the case where the corresponding part of the boundary degenerates, the Robin–Neumann radius is considered. The monotonicity of the p-harmonic Robin radius under some deformations of a domain is proved. Some extremal decomposition problems in the Euclidean space are solved. The definitions and proofs are based on the technique of moduli of curve families. Bibliography: 23 titles.