Banach空间L^P(Ω)中非齐次不适定椭圆边值问题的最小范数极值解

The Minimal Norm Extrimal Solution to the Non-Homogeneous Ill-Posed Boundary Value Problem in Banach Space L^p(Ω)

该文对 Ｂａｎａｃｈ空间 ＬＰ（Ω）中二阶椭圆方程非齐次不适定 Ｎｅｕｍａｎｎ 问题，引入伪变分解的概念，应用Ｂａｎａｃｈ空间几何及［３］中关于Ｂａｎａｃｈ空间中线性算子的Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ广义逆．证明了上述伪变分解为最小范数极值解，从而为适定的．

In this paper, the concept of preudo variational solution to the non-homogeneous ill-posed Neumann boundary value problem has been introduced in Banach space L^p(Ω) By means of mathod of Geometry of Banach space and Moore-Penrose metric generalized inverse of the linear operator in Banach space, we have proved that the preudo variational solution is well posed, and is equivvalent to the minimal norm extrimal solutionn to the boundary value problem in L^p(Ω).