  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 $\Omega$.
