| The generalized solution of ill-posed boundary problem |
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| 作者姓名： | CAO Weiping & MA Jipu |
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| 作者单位： | CAO Weiping & MA Jipu Department of Mathematics and Physics，Huaihai Institute of Technology，Lianyungang 222005，China; Y. Y. Tseng Functional Analysis Research Centre，Harbin Normal University，Harbin 150080，China |
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| 基金项目： | 国家自然科学基金;国家自然科学基金 |
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| 摘 要： | In this paper, we define a kind of new Sobolev spaces, the relative Sobolev spaces Wk,p0(Ω,∑). 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.
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| 收稿时间： | 30 September 2005 |
| 修稿时间： | 16 March 2006 |
The generalized solution of ill-posed boundary problem |
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| CAO Weiping & MA Jipu.The generalized solution of ill-posed boundary problem[J].Science in China(Mathematics),2006,49(7):902-911. |
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| Authors: | CAO Weiping MA Jipu |
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| Institution: | 1. Department of Mathematics and Physics, Huaihai Institute of Technology, Lianyungang 222005, China
2. Y. Y. Tseng Functional Analysis Research Centre, Harbin Normal University, Harbin 150080, China |
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| Abstract: | In this paper, we define a kind of new Sobolev spaces, the relative Sobolev spaces W
0
k,p
(Θ, 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. |
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| Keywords: | generalized inverse of operator generalized solution ill-posed boundary problem elliptic partial differential equations of second order |
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