Existence of minimizers for Schrodinger operators under domain perturbations with application to Hardy's inequality Yehuda PinchoverKyril Tintarev 35J7035J2049R50concentration compactnessgap phenomenonHardy inequalityprincipal eigenvalue The paper studies the existence of minimizers for Rayleigh quotients % $\mu_{\Omega}=\inf\displaystyle\int_{\Omega}|\nabla % u|^2\dx/\displaystyle\int_{\Omega}V{|u|^2}\dx$, \[ \mu_{\Omega}=\inf\frac{\displaystyle\int_{\Omega}|\nabla u|^2\dx}{\displaystyle\int_{\Omega}V{|u|^2}}\dx, \] where $\Omega$ is a domain in $\mathbb{R}^N$, and $V$ is a nonzero nonnegative function that may have singularities on $\partial\Omega$. As a model for our results one can take $\Omega$ to be a Lipschitz cone and $V$ to be the Hardy potential $V(x)=1/|x|^2$. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2705 10.1512/iumj.2005.54.2705 en Indiana Univ. Math. J. 54 (2005) 1061 - 1074 state-of-the-art mathematics http://iumj.org/access/