高阶一致椭圆型算子带权第二特征值的上界估计(英文)

Estimation of the upper bound of the second eigenvalue with weight for uniformlyelliptic operator with high orders

考虑高阶一致椭圆型算子带权第二特征值的上界估计.利用试验函数、Rayleigh定理、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的不等式,其估计系数与区间的度量无关.

Upper bound estimation of second eigenvalue with weight for uniformly elliptic operator with high orders was considered. The inequality of the upper bound of the second eigenvalue was deduced from the first eigenvalue by means of testing function, Rayleigh theorem, partial integration and Schwarz inequality. The estimate coefficients do not depend on the measure of the domain in which the problem is concerned.