Hardy-type inequalities and principle frequency of the $p-$Laplacian

Bo-Yong Chen

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arXiv · 2007.06782

Hardy-type inequalities and principle frequency of the $p-$Laplacian

Bo-Yong Chen

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Abstract

We prove a sharp $L^p$ weighted Hardy inequality involving boundary distance $\delta$ for any domain $\Omega\subsetneq \mathbb R^n$. The inequality may be improved substantially under the additional assumption that $-\log \delta$ is subharmonic. Applications of these inequalities to the principle frequency of the $p-$Laplacian are given.

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Bo-Yong Chen. 2020-07-14. Hardy-type inequalities and principle frequency of the $p-$Laplacian. https://arxiv.org/abs/2007.06782

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