黎曼流形上一类算子的特征值不等式

INEQUALITIES FOR EIGENVALUES OF A CLASS OF OPERATORS ON RIEMANNIAN MANIFOLDS

本文研究了等距浸入欧氏空间的黎曼流形、容许特殊函数的黎曼流形上的一类椭圆算子的加权狄利克雷特征值问题.我们建立了该问题的一些万有特征值不等式.同时,作为应用,我们获得了拉普拉斯算子的二次多项式算子的加权狄利克雷问题的一些结果.

In this paper,we investigate the weighted Dirichlet eigenvalue problem of a class of operators on Riemannian manifolds isometrically immersed into a Euclidean space and Riemannian manifolds admitting some special functions.We establish some universal inequalities for eigenvalues of this problem.Moreover,as applications,we derive some results for the weighted Dirichlet eigenvalue problem of quadratic polynomial operator of the Laplacain.