Characterization of balls through optimal concavity for potential functions

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.

References in corpus (1)

• Symmetry of minimizers with a level surface parallel to the boundary

Cited by in corpus (2)

• A note on an overdetermined problem for the capacitary potential
• Optimal concavity of the torsion function