An extremum theory of the residual functional in Sobolev spacesW m,p(ω)
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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.
Key wordsSobolev spaces residual functional infinite Banach spaces convex lower semi-continuity force condition minimum existence theorem
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