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(guó)科學(xué)A輯（英文版）  SCI 英文刊名： SCIENCE IN CHINA SERIES A  年，卷(期)： 2006 49(7)  分類號(hào)： O1  關(guān)鍵詞： generalized inverse of operator   generalized solution   ill-posed boundary problem   elliptic partial differential equations of second order  

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