Asymptotic behaviour of the first eigenfunction of a Hardy-Sobolev operator. (Q1395867)

Let \(\Omega\) be a bounded domain in \(\mathbb R^N\) with \(N\geq 3\) and \(L\) denotes the Hardy-Sobolev operator given by \[ Lu:= -\Delta u- \bigg(\frac{n-2}{2}\bigg)^2 \frac{q(x)u}{|x|^2}, \quad u\in H_0^1(\Omega). \] The author is mainly interested in studying the singularity of the first eigenfunction of \(L\).