一类极大值问题的上确界

The Supremum of a Class of Maximum Value Problems

设Ω为R^N（N≥3）中的有界光滑区域,p=（N+2）/（N-2）。我们证明了:存在常数λ≥0使得λ>λ时,下列极大值问题的上确界能够达到;当λ<λ时该极大值不能达到,特别地有:当N≥4时,λ=0,当N=3时,λ>0。

Let be a smooth bounded domain in RN(N >3),P =N+2/N-2.In this paper, the following maxi-mum value problem posed by H. Brezis is concerned :We prove that there exists some constant such that M can be attained provided and will never be attained if that .