二阶线性椭圆型方程广义解的群对称分析  

Analysis of Group Symmetry of Generalized Solutions for Second-Order Linear Elliptic Equations

作　　者：陈泽彬 CHEN Zebin(Shenzhen Metro Group Co.,Ltd.,Shenzhen,Guangdong Province,518040 China)

机构地区：[1]深圳地铁运营集团有限公司,广东深圳518040

出　　处：《科技资讯》2024年第21期233-235,共3页Science & Technology Information

摘　　要：Lie群变换方法从研究一般偏微分方程(Partial Differential Equations, PDE)的定性理论,推广到一般二阶线性椭圆型方程广义解(弱解)的存在性与正则性的研究中。从一般类型的方程而非最古典、特殊的Poisson方程入手,首次得到一般二阶线性椭圆型PDE的Lie群对称性。并运用相关估计理论,分析其Dirichlet问题的广义解的存在性所受到方程对称性的影响,以及保持广义解的正则性所对应的对称形式,最终在局部或全局上揭示广义解与方程对称性之间的关系。The Lie group transformation method has been extended from studying the qualitative theory of general Partial Differential Equations(PDE)to studying the existence and regularity of generalized solutions(weak solu-tions)of general second-order linear elliptic equations.Starting from general types of equations rather than the most classical and special Poisson equations,the Lie group symmetry of general second order linear elliptic PDE is obtained for the first time.Relevant estimation theory is applied to analyze the influence of equation symmetry on the existence of generalized solutions of Dirichlet problems,as well as the symmetric form corresponding to main-taining the regularity of generalized solutions.Finally,the relationship between generalized solutions and equation symmetry is revealed locally or globally.

关 键 词：二阶线性椭圆型方程 广义解 群对称性 正则性 

分 类 号：O171[理学—数学]