Sobolev空间W^m,p（Ω）中残差泛函的极值理论

本文在Sobolev空间中讨论残差泛函J(u)的概念及性质,论证了残差泛函J(u)的弱紧性、强制性和下半连续性及凸性条件.根据临界点理论在Sobolev空间中建立起该残差泛函的极值原理,给出J(u)=0极小值存在定理.此外还证明了等价定理和J(R_n(c))=0的五种等价形式.     

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES Wm,p（Ω）

In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreom for J(u)=0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.     

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES W~(m,p)t(Ω)

In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreom for J(u)=0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.