The generalized solution of ill-posed boundary problem  

作　　者：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 

出　　处：《Science China Mathematics》2006年第7期902-911,共10页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10171087);the Science Foundation of Jiangsu Province(Grant No.01KJD110010).

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.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.

关 键 词：GENERALIZED INVERSE of operator  GENERALIZED solution  ILL-POSED boundary problem  ELLIPTIC partial differential EQUATIONS of second order. 

分 类 号：O175.8[理学—数学]