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arXiv · 2207.14582

An isoperimetric result for an energy related to the $p$-capacity

Paolo Acampora·Emanuele Cristoforoni
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Abstract

In this paper, we generalize the notion of relative $p$-capacity of $K$ with respect to $\Omega$, by replacing the Dirichlet boundary condition with a Robin one. We show that, under volume constraints, our notion of $p$-capacity is minimal when $K$ and $\Omega$ are concentric balls. We use the $H$-function and a derearrangement technique.

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Paolo Acampora, Emanuele Cristoforoni. 2022-07-29. An isoperimetric result for an energy related to the $p$-capacity. https://doi.org/10.4171/rlm%2F1030

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