高阶一致椭圆型算子第二特征值上界估计的不等式  

Inequality of Estimate of Upper Bound of Second Eigenvalue for Uniformly Elliptic Operator with High Orders

作　　者：赵晓苏[1] 钱椿林[1] Zhao Xiaosu;Qian Chunlin(Department of Mathematical and Physics,Suzhou Vocational University,Suzhou,Jiangsu 214104,China)

机构地区：[1]苏州市职业大学数理部,江苏苏州215104

出　　处：《黑龙江工业学院学报（综合版）》2020年第7期44-52,共9页Journal of Heilongjiang University of Technology(Comprehensive Edition)

摘　　要：考虑高阶一致椭圆型算子第二特征值的上界估计的问题,即等式一端是高阶一致椭圆型算子,等式另一端是r阶一致椭圆型算子的第二特征值上界估计的问题。使用试验函数,Rayleigh定理,数学归纳法,分部积分和Schwarz不等式等估计方法和技巧,获得了可由第一特征值估计第二特征值上界的估计不等式,该估计系数与区域的几何度量无关。其结果在力学和微分方程的研究中有着广泛的应用。This paper considers the estimate of the upper bound of second eigenvalue for uniformly elliptic operator with high orders,That is,the left end of the equality is a uniformly elliptic operator of high order,and the right end of the equality is the second eigenvalue estimation of a r-order uniformly elliptic operator.The inequality of upper of second eigenvalue is deduced from first eigenvalue by using testing function,Rayleigh theorem,mathematical induction,partial integration and Schwarz inequality.The estimate coefficients do not depend on the geometric measure of the domain in which the problem is concerned.The result is widely used in the study of mechanics and differential equation.

关 键 词：高阶一致椭圆型算子 不等式 特征值 特征函数 上界 估计 

分 类 号：O175.1[理学—数学]