带权的贝塞尔位势积分方程解的对称性  

Symmetry of Solutions to Weighted Bessel Potential Integral Equations

作　　者：王昊峰 李云亭 廖秋萍 易云辉 Wang Haofeng;Li Yunting;Liao Qiuping;Yi Yunhui(School of Mathematics and Computer Science,Jiangxi Science and Technology Normal University,Nanchang 330038,Jiangxi,P.R.China)

机构地区：[1]江西科技师范大学数学与计算机科学学院,江西南昌330038

出　　处：《江西科技师范大学学报》2022年第6期112-116,共5页Journal of Jiangxi Science & Technology Normal University

基　　金：江西省教育厅重点项目(GJJ211101);江西科技师范大学研究生创新专项资金项目(YC2022-X01、YC2022-X09)。

摘　　要：本文主要研究了带权的贝塞尔位势的积分方程。在整体可积的假设下,将单个带权的积分方程转化成方积分程组进行研究。利用移动平面法、Hardy-Littlewood-Sobolev不等式和H?lder不等式、贝塞尔位势和Riesz位势的关系等方法,证明了带权的贝塞尔位势积分方程解具有径向对称性和单调性。This paper mainly studies the integral equation of the weighted Bessel potential. Under the assumption of overall integrability, this paper transformed the above single integral equation into a system of integral equations for research. By using the moving plane method, Hardy-Littlewood-Sobolev inequality and H?lder inequality, the relationship of Bessel potential and Riesz potential and other conceptual methods, it is proved that the radial symmetry and monotonicity of the solution of the weighted Bessel potential integral equation.

关 键 词：贝塞尔位势 移动平面法 径向对称性 积分方程组 

分 类 号：O175.2[理学—数学]