位势方程的Robin问题解的研究  

Study on Robin Problem Solution for Potential Equation

作　　者：金庆飞 JIN Qingfei(School of Artificial Intelligence,Jianghan University,Wuhan 430056,Hubei,China)

机构地区：[1]江汉大学人工智能学院,湖北武汉430056

出　　处：《江汉大学学报（自然科学版）》2023年第1期5-9,共5页Journal of Jianghan University：Natural Science Edition

基　　金：江汉大学科研启动经费项目(1028/06050001)。

摘　　要：位势方程是偏微分方程理论研究中的一类典型的二阶椭圆型方程。对位势方程的Robin问题作了深入研究,运用散度定理证明了该问题在C^(1)(-Ω)∩C^(2)(Ω)中解的唯一性,并运用Green函数法导出该问题的Green函数G(x,y)满足的条件和该问题的解的表达式。The potential equation is a typical second-order elliptic equation in the theoretical research of partial differential equations.In this paper,the Robin problem of the potential equation was studied deeply.We proved the uniqueness of its solution in C^(1)(-Ω)∩C^(2)(Ω) by the divergence theorem.The conditions satisfied by the Green′s function G(x,y)and the expression of its solution were derived by Green′s function method.

关 键 词：位势方程 ROBIN问题 GREEN函数 椭圆型方程 

分 类 号：O186.1[理学—数学]