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