一类积分方程组的部分超定问题  

Partial Overdetermination of Some Integral Equation Systerms

作　　者：蔡贵 易福侠[2] CAI Gui;YI Fu-xia(School of Mathematics and Information Sciences,Nanchang Hangkong University,Nanchang 330063,China;Department of Fundational Courses,Jiangxi V&T College of Communiction, Nanchang 330013,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063 [2]江西交通职业技术学院基础课部,南昌330013

出　　处：《南昌航空大学学报（自然科学版）》2018年第3期26-34,共9页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：江西省教育厅科学技术研究项目(GJJ171294;GJJ160719)

摘　　要：研究了有界域上关于Riesz位势型积分方程组部分超定问题的对称性问题。首先,假设积分方程组部分超定问题的正解存在且满足一定的可积性,以此证明了解的存在区域是一个球,证明中同时得到了正解的径向对称性以及关于半径单调递减的性质。The partial overdetermined problem of integral equations with Riesz potential on bounded domain was investigated in this paper. Under some natural integrability conditions on the positive solution to the partial overdetermined problem of integral equations,we obtained that the domain is a ball. Moreover,the solution is radially symmetric and monotone decreasing with respect to the radius.

关 键 词：积分方程组 部分超定问题 移动平面法 对称性 

分 类 号：O175.2[理学—数学] O175.6[理学—基础数学]