柱形域上的Riesz位势积分方程组超定问题的对称性  

Symmetry of An Integral System with Risez Potential in the Cylinder Type Domain

作　　者：吕博强 谭秀兰 蔡贵 LV Bo-qiang;TAN Xiu-lan;CAI Gui(School of Mathematics and Information Sciences,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院

出　　处：《南昌航空大学学报（自然科学版）》2019年第3期17-24,共8页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(11601218);江西省教育厅科技项目(GJJ171294)

摘　　要：考虑上无界柱形域的一类Riesz位势积分方程组,一方面,证明了超定问题正解存在时柱形域是圆柱且解轴对称;另一方面,如果部分边界条件具有一定几何条件,证明了部分超定问题相应的区域和解的对称性。首次给出了上无界柱形域积分方程组超定问题的对称结果,推广并改进了现有单个方程的结果。This paper studies the overdetermined problem for the integral system with Riesz potential in cylinder type domain.On the one hand,we show that the cylinder type domain is indeed a cylinder and the solution is also rotationally symmetric with respect to the cylinder axis provide that the standard overdetermined problem admits a positive solution.On the other hand,under some requirements on the geometry for the partial boundary,we illustrate that the partial overdetermined problem also satisfies the symmetry of the domain and the solution.This paper first shows the symmetry of integral system in the unbounded cylinder type domain,which generalized the similar results for the single equation.

关 键 词：无界柱形域 Riesz位势积分方程组 超定问题 

分 类 号：O175.2[理学—数学]