Optimal $L^p$ Hardy inequalities

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1 TECHNION - Department of Mathematics

Abstract : Let $\mathcal{Q}\varphi:=\int \Omega \big| abla \varphi|^p+V|\varphi|^p\big\dnu$ on $\core$, and assume that $\mathcal{Q}\geq 0$. The aim of the paper is to obtain -as large as possible- nonnegative optimal Hardy-type weight $W$ satisfying $$\mathcal{Q}\varphi\geq \int {\Omega} W|\varphi|^p\dnu \quad\forall \varphi\in\core,$$ on punctured domains $\Omega$.

Keywords : Hardy inequality optimal p-Laplacian

Author: Baptiste Devyver - Yehuda Pinchover -

Source: https://hal.archives-ouvertes.fr/