Optimal $L^p$ Hardy inequalities

Baptiste Devyver (1) , Yehuda Pinchover (1)

1 TECHNION - Department of Mathematics

Let $\mathcal{Q}(\varphi):=\int_\Omega \big(|\nabla \varphi|^p+V|\varphi|^p\big)\dnu$ 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 $\Omega$.

Mots clés: Hardy inequality; optimal; p-Laplacian

Domaines: Equations aux dérivées partielles [math.AP]

Baptiste Devyver, Yehuda Pinchover. Optimal $L^p$ Hardy inequalities. 2013. ⟨hal-00921684⟩