On the Brézis–Nirenberg Problem
On the Brézis–Nirenberg Problem
We study the following Brézis–Nirenberg problem (Comm Pure Appl Math 36:437–477, 1983): $$-\Delta u=\lambda u+ |u|^{2^\ast-2}u, \quad u\in H_0^1(\Omega),$$ where Ω is a bounded smooth domain of R N (N ≧ 7) and 2* is the critical Sobolev exponent. We show that, for each fixed λ > 0, this problem …