Ling Yong-yong. An Extremum Theory of the Residual Functional in Sobolev Spaces Wm, p(Ω)[J]. Applied Mathematics and Mechanics, 1992, 13(3): 255-262.
Citation: Ling Yong-yong. An Extremum Theory of the Residual Functional in Sobolev Spaces Wm, p(Ω)[J]. Applied Mathematics and Mechanics, 1992, 13(3): 255-262.

An Extremum Theory of the Residual Functional in Sobolev Spaces Wm, p(Ω)

  • Received Date: 1990-12-24
  • Publish Date: 1992-03-15
  • 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 theoreomfor 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.
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