任意阶一致椭圆型算子第二特征值的上界估计  

Estimate of Upper Bound of the Second Eigenvalue for Uniformly Elliptic Operator with Arbitrary Order

作　　者：赵晓苏[1] 钱椿林[1] ZHAO Xiaosu;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

出　　处：《长春大学学报》2019年第10期16-22,共7页Journal of Changchun University

摘　　要：考虑任意阶一致椭圆型算子第二特征值的上界估计的问题,即等式左端是任意阶一致椭圆型算子,等式右端是四阶一致椭圆型算子的第二特征值估计的问题。利用试验函数,Rayleigh定理,数学归纳法,分部积分和Schwarz不等式等估计方法与技巧,获得了用第一特征值来估计第二特征值的上界估计的不等式,其估计系数与区域的几何度量无关。其结果在物理学和力学中有着广泛的应用,在微分方程的研究中起着重要的作用。This paper considers the estimate of the upper bound of the second eigenvalue for uniformly elliptic operator with arbitrary order,namely,the second eigenvalue estimation problem that the left end of the equality is a uniformly elliptic operator with arbitrary order and the right end of the equality is a uniformly elliptic operator with fourth-order. The inequality of upper estimate 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. The results are widely applied in physics and mechanics,and play an important role in the study of differential equations.

关 键 词：任意阶一致椭圆型算子 特征值 特征函数 上界 估计 

分 类 号：O175.1[理学—数学]