Optimal Hardy inequalities in cones

Baptiste Devyver, Yehuda Pinchover, Georgios Psaradakis

Let $\Omega$ be an open connected cone in ${\mathbb{R}}^n$ with vertex at the origin. Assume that the operator $$P_{\mu }:=-\Delta -\frac{\mu }{{\delta }_{\Omega }^2(x)}$$ is {\em subcritical} in $\Omega$, where ${\delta }_{\Omega }$ is the…