Classification of solutions of a critical Hardy–Sobolev operator

AbstractIn this article we classify all positive finite energy solutions of the equation -Δu=unn-2|y| in Rn where Rn=Rk×Rn-k,n>k⩾2 and a point x∈Rn is denoted as x=(y,z)∈Rk×Rn-k. As a consequence we obtain the best constant and extremals of a related Hardy–Sobolev inequality