Applied Mathematics and Mechanics

, Volume 13, Issue 3, pp 273–279 | Cite as

An extremum theory of the residual functional in Sobolev spacesW m,p(ω)

  • Ling Yong-yong
Article
  • 11 Downloads

Abstract

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 words

Sobolev spaces residual functional infinite Banach spaces convex lower semi-continuity force condition minimum existence theorem 

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Copyright information

© Shanghai University of Technology (SUT) 1992

Authors and Affiliations

  • Ling Yong-yong
    • 1
  1. 1.Department of Applied MathematicsTongji UniversityShanghai

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