Equivalence between validity of the $p$-Poincar\'e inequality and finiteness of the strict $p$-capacitary inradius

A. -K. Gallagher

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arXiv · 2404.19207

Equivalence between validity of the $p$-Poincar\'e inequality and finiteness of the strict $p$-capacitary inradius

A. -K. Gallagher

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Abstract

It is shown that the $p$-Poincar\'e inequality holds on an open set $\Omega$ in $\mathbb{R}^n$ if and only if the strict $p$-capacitary inradius of $\Omega$ is finite. To that end, new upper and lower bounds for the infimum for the associated nonlinear Rayleigh quotients are derived.

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A. -K. Gallagher. 2024-04-30. Equivalence between validity of the $p$-Poincar\'e inequality and finiteness of the strict $p$-capacitary inradius. https://arxiv.org/abs/2404.19207

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