An Extremum Theory of the Residual Functional in Sobolev Spaces W<sup>m, p</sup>(Ω)

Ling Yong-yong

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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 W^{m, p}(Ω)[J]. Applied Mathematics and Mechanics, 1992, 13(3): 255-262.

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 W^{m, p}(Ω)[J]. Applied Mathematics and Mechanics, 1992, 13(3): 255-262.

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An Extremum Theory of the Residual Functional in Sobolev Spaces W^{m, p}(Ω)

Ling Yong-yong

Department of Applied Mathematics, Tongji University, Shanghai

Received Date: 1990-12-24
Publish Date: 1992-03-15

Abstract

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

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References(11)

References

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