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)

• 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.
•  [1] 第三届全国加权残值法会议论文集,西南交通大学出版社(1989). [2] 徐次达.固体力学加权残值法,同济大学出版社(1987), [3] 邱吉宝,加权残数法理论基础的初步探讨,力学学报,19SUP (1987), [4] 凌铺墉,一类非线性微分方程的残差不等式,第三届全国加权残值法会议论文集,西南交通大学出版社(1989), 38 [5] 凌铺铺.凌满储,二阶非线性微分方程周期解及误差界估计,第一届全国解析与数值结合法会议论文集,湖南大学出版社(1990), 853, [6] Adams, R,A 《Sobolev空间》,北京大学数学系译(1977), [7] 李立康、郭毓殉,《索伯列夫空间引论》.上海科技出版社(1981), [8] 张恭庆,《临界点理论及其应用》(现代数学丛书).上海科学技术出版社(1986), [9] Lipschutz, S,,《一般拓扑学》,华东师范大学出版社(1982), [10] Ciesielski, Z.and J, Domsta, Construction of anorthonormal basis in Cm(Id) and Wpm(Id),Studia Math.,41 (1972), 211, [11] Mitrinovié, D, S.《解析不等式》,科学出版社(1987),

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142