The authors prove some refined asymptotic estimates for positive blow-up solutions to \(\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}\) on \(\Omega\), \(\partial_\nu u=0\) on \(\partial\Omega\), \(\Omega\) being a smooth bounded domain of \(\mathbb{R}^n\), \(n\geq 3\). In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when \(n=3\) or \(n\geq 7\). As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension \(n=3\) and \(n\geq 7\) for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.