四阶一致椭圆型算子第二特征值的上界估计(英文)

Estimate of the upper bound of second eigenvalue for uniformly elliptic operator with four orders

研究了四阶一致椭圆型算子第二特征值的上界估计.利用试验函数、Rayleigh定理、分部积分、Schwartz不等式和Young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,上界与区域的几何度量无关.

The estimate of the upper bound of the second eigenvalue for the uniformly elliptic operator with four orders was studied. By means of integral, Rayleigh theorem and inequalities, it was obtained that the upper bounds of the second eigenvalue are dependent on the first eigenvalue but not the measure of the domain in which the problem is concerned.