Lower order eigenvalues of a system of equations of the drifting Laplacian on the metric measure spaces
Lower order eigenvalues of a system of equations of the drifting Laplacian on the metric measure spaces
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DOI：
10.1007/s00013-017-1131-3
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发表时间：
2018-01
影响因子：
0.6
通讯作者：
He-Jun Sun
中科院分区：
文献类型：
--
作者：
He-Jun Sun
Letbe a bounded domain with smooth boundary in ann-dimensional metric measure spaceand letbe a vector-valued function fromto. In this paper, we investigate the Dirichlet eigenvalue problem of a system of equations of the drifting Laplacian:, in, andwhereis the drifting Laplacian andis a nonnegative constant. We establish some universal inequalities for lower order eigenvalues of this problem on the metric measure spaceand the Gaussian shrinking soliton. Moreover, we give an estimate for the upper bound of the second eigenvalue of this problem in terms of its first eigenvalue on the gradient product Ricci soliton, whereis an Einstein manifold with constant Ricci curvature.
