Extremal decomposition problems for p-harmonic radius

Sergei Kalmykov; Elena Prilepkina

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arXiv · 1604.05230

Extremal decomposition problems for p-harmonic radius

Sergei Kalmykov·Elena Prilepkina

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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, $n \geq 3$, 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.

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Sergei Kalmykov, Elena Prilepkina. 2016-04-18. Extremal decomposition problems for p-harmonic radius. https://arxiv.org/abs/1604.05230

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