Sobolev空间中集值映射不动点的连续选择(Ⅰ)——连续选择定理  

Continuous Selection of Fixed Points of Set-Valued Map in Sobolev Space(Ⅰ)——Continuous Selection Theorem

作　　者：孙广毅[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2002年第1期139-142,共4页Journal of Harbin Engineering University

摘　　要：在Sobolev空间中利用Lebesgue积分引入了一种函数 ,给出了该函数连续的条件 ,证明了该函数是Sobolev空间上的连续半范 .在此基础上 ,建立了Sobolev空间中一类集值映射连续选择的存在性定理 。A function is introduced by Lebesgue's integral, and the criteria are given for the continuity of this function, and it is proved that this function is the continuous seminorm in Sobolev space. From this, the existence of continuous selection has been established for a class of set_valued mappings with values in Sobolev space. Further results are obtained for continuous selections as the corollaries.

关 键 词：Soboley空间 集值映射 不动点 连续选择 连续选择定理 可分解性 

分 类 号：O177.8[理学—数学]