一类偏微分系统离散谱的带权估计

Weighted Estimates for Discrete Spectrum of a Partial Differential System

考虑一类偏微分系统离散谱的带权估计,利用分部积分、Rayle igh定理和不等式估计等方法和技巧,获得了用前n个特征值来估计第n+1个特征值的上界的不等式,其估计系数与区域的几何度无关,其结果在物理和力学等领域中应用广泛。

This paper considers weighted estimates for discrete spectrum of a partial differential system. The inequality of the upper bound of the （ n ＋ 1 ） th eigenvalue is estimated from the first n eigenvalues by using integral, Reyleigh theorem and inequality estimation. The estimate coefficients do not depend on the measure of the domain in which the problem is concerned. The result is widely used in physics and mechanics.