关于Laplace方程Neumann问题伪解的连续相依性  

On Continuous Dependence Property of Pseudosolution to Neumann Problem for Laplace Equation

作　　者：谢忠林[1] 

机构地区：[1]哈尔滨科技大学

出　　处：《辽宁师范大学学报（自然科学版）》1990年第4期15-19,共5页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：本文在空间L^p(Ω)(2≤p≤2n/(n-2))中讨论Laplace方程的Neumann问题: 这里f∈L^q(Ω).如所周知,对f∈L^q(Ω)(1/p+1/q=1),此边值问题一般是不适定的。为克服这一困难,引入伪解的概念,并证得伪解的存在性与唯一性。本文继续这一工作,证得伪解关于强制项是连续相依的,从而使问题成为适定的。We discuss Neumann problem for Laplace equation in space L^P(Ω)(2≤p≤2n/(n-2)),where f∈L^q(Ω)(1/p+1/q=1).It is well known that for any f∈L^q(Ω),the boundary Problem is generally ill-posed.To overcome this difficulty,the Concept of pseudo-solution is introduced,and continuous dependence of it is proved in this paper,so that the problem becomes well-posed.

关 键 词：LAPLACE方程 适定问题 伪解 

分 类 号：O175.25[理学—数学]