关于空间H_0~1(Ω)和W_0^(1,p)(Ω)的对偶空间表示的注记

A Note about Representation of the DualSpace of Space H_0~1(Ω) and W_0^(1,p)(Ω)

通过研究H_0~1(Ω)的对偶空间H^(-1)(Ω),发现H^(-1)(Ω)的Riesz表示唯一,但在(L2(Ω))N+1中的表示不唯一.同样地,对于W_0^(1,p)(Ω)的对偶空间W-1,p'(Ω),在W_0^(1,p)(Ω)有唯一表示,但在(Lp'(Ω))N+1中的表示不唯一.

By studying the dual space H-1(Ω)of H01(Ω),we find that the Riesz representation of H-1(Ω)is unique,but not unique in(L2(Ω))N+1.Similarly,for the dual space W-1,p’(Ω)of W01,p(Ω),W-1,p’(Ω)has unique representation in W01,p(Ω),but not unique in(Lp’(Ω))N+1.