On existence of minimizers for the Hardy-Sobolev-Maz'ya inequality

Achilles Tertikas, Kyril Tintarev

We show existence of minimizers for the Hardy-Sobolev-Maz'ya inequality in $R^{m+n}\setminus {\mathbb{R}}^n$ for $m=1$ and $n>2$ or for $m>2$ and $n>0$.