Lower order eigenvalues of Dirichlet Laplacian |
| |
Authors: | Hejun Sun Qing-Ming Cheng Hongcang Yang |
| |
Institution: | (1) Department of Applied Mathematics, College of Science, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China;(2) Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan;(3) Academy of Mathematics and Systematical Sciences, CAS, Beijing, 100080, China |
| |
Abstract: | In this paper, we investigate an eigenvalue problem for the Dirichlet Laplacian on a domain in an n-dimensional compact Riemannian manifold. First we give a general inequality for eigenvalues. As one of its applications,
we study eigenvalues of the Laplacian on a domain in an n-dimensional complex projective space, on a compact complex submanifold in complex projective space and on the unit sphere.
By making use of the orthogonalization of Gram–Schmidt (QR-factorization theorem), we construct trial functions. By means
of these trial functions, estimates for lower order eigenvalues are obtained.
Qing-Ming Cheng research was partially supported by a Grant-in-Aid for Scientific Research from JSPS.
Hejun Sun and Hongcang Yang research were partially supported by NSF of China. |
| |
Keywords: | 35P15 58C40 |
本文献已被 SpringerLink 等数据库收录! |
|