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arXiv · 1210.6274

Characterization of balls through optimal concavity for potential functions

Paolo Salani
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Abstract

Let $p\in(1,n)$. If $\Omega$ is a convex domain in $\rn$ whose $p$-capacitary potential function $u$ is $(1-p)/(n-p)$-concave (i.e. $u^{(1-p)/(n-p)}$ is convex), then $\Omega$ is a ball.

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Paolo Salani. 2012-10-23. Characterization of balls through optimal concavity for potential functions. https://doi.org/10.1090/s0002-9939-2014-12196-4

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