拉普拉斯算子多项式第二特征值估计的不等式  

Estimate Inequality of Second Eigenvalues for Polynomials of the Laplacian Operator

作　　者：杨晓华[1] 钱椿林[1] YANG Xiaohua;QIAN Chunlin(Department of Mathematics and Physics,Suzhou Vocational University,Suzhou 215104,China)

机构地区：[1]苏州市职业大学数理部,江苏苏州215104

出　　处：《苏州市职业大学学报》2018年第4期46-50,共5页Journal of Suzhou Vocational University

基　　金：苏州市职业大学成果创新项目(2013SZDCC11)

摘　　要：考虑拉普拉斯算子多项式的第二特征值上界估计。利用变分法、Rayleigh定理、分部积分、Schwartz不等式和Young不等式等估计方法与技巧,获得了用第一特征值来估计第二特征值的上界的不等式,上界与区域的几何度量无关,很多结果都是本文的特例。Considered are estimates for the upper bounds of eigenvalues to a kind of polynomials of the Laplacian operator.By using the variation method,integral,Rayleigh theorem and inequalities,it is found that the upper bounds of the second eigenvalue is dependent on the first eigenvalue and do not depend on the measure of the domain in which the problem is concerned.Many results of this kind of estimates can be deduced as special cases from the results in this paper.

关 键 词：多项式 拉普拉斯算子 特征值 特征函数 上界 估计 

分 类 号：O175.1[理学—数学]