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The generalized solution of ill-posed boundary problem
In this paper, we define a kind of new Sobolev spaces, the relative Sobolev spaces Wk0,p(Ω, Σ). Then an elliptic partial differential equation of the second order with an ill-posed boundary is discussed. By utilizing the ideal of the generalized inverse of an operator, we introduce the generalized solution of the ill-posed boundary problem. Eventually, the connection between the generalized inverse and the generalized solution is studied. In this way, the non-instability of the minimal normal least square solution of the ill-posed boundary problem is avoided.
作 者： CAO Weiping MA Jipu 作者單位： CAO Weiping(Department of Mathematics and Physics, Huaihai Institute of Technology, Lianyungang 222005, China)MA Jipu(Y. Y. Tseng Functional Analysis Research Centre, Harbin Normal University, Harbin 150080, China)
刊 名： 中國科學A輯（英文版） SCI 英文刊名： SCIENCE IN CHINA SERIES A 年，卷(期)： 2006 49(7) 分類號： O1 關(guān)鍵詞： generalized inverse of operator generalized solution ill-posed boundary problem elliptic partial differential equations of second order【The generalized solution of ill-pose】相關(guān)文章：
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