Rellich-Poincaré inequalities and improved Rellich inequalities

We study linear variational problems on bounded domains $Ω\subset \mathbb R^d$ involving the Dirichlet biharmonic operator $Δ^{2}$ and the Rellich potential $|x|^{-4}$, under the assumption $0\in\overlineΩ$. The case $0\in\partialΩ$ is particularly noteworthy and subtle.