Sobolev空间Wm, p(Ω)中残差泛函的极值理论
An Extremum Theory of the Residual Functional in Sobolev Spaces Wm, p(Ω)
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摘要: 本文在Sobolev空间中讨论残差泛函J(u)的概念及性质,论证了残差泛函J(u)的弱紧性、强制性和下半连续性及凸性条件.根据临界点理论在Sobolev空间中建立起该残差泛函的极值原理,给出J(u)=0极小值存在定理.此外还证明了等价定理和J(R,sub>n(c))=0的五种等价形式.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.
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[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), -
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