多重调和算子组高阶特征值的定量分析

Quantitative Analysis of Higher-Order Eigenvalue for System of Poly-harmonic Operators

对多重调和算子组高阶特征值进行带权估计,利用算子特征值理论、向量和矩阵运算、分部积分、测试函数和Rayleigh原理等方法,获得了用前n个特征值来估计第n+1个特征值上界的一个隐式和一个显式不等式,其界与空间维数及权函数有关,而与所论区域的度量无关,其结论进一步拓展了相关文献的结果。

This paper describes weighted estimate of higher-order eigenvalue for system of poly-harmonic operators, estimating both implicit and explicit inequalities of the upper bound of the(n+1)th eigenvalue from the former n eigenvalues by using eigenvalue theory of operators, vector and matrix operation, integration by parts, trial function and Rayleigh theorem etc., which bound is dependent of the space dimension and weight function, but is independent on the measure of the domain in which the problem is concerned. The results expand the theorems in the bibliography.