Characterization of concentration points and L^∞-estimates for solutions of a semilinear neumann problem involving the critical sobolev exponent

Let Ω ⊂ Rⁿ(n≥7) be a bounded domain with smooth boundary. For λ > 0, let uλ be a solution of-Δu + λu = u n+2/n-2 in Ω, u > 0 in Ω, ∂u/∂v = 0 on ∂Ω, whose energy is less than the first critical level. Here we study the blow up points and the L∞-estimates of uλ as λ → ∞. We show that the blow up points are the critical points of the mean curvature on the boundary.