Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds
We investigate the Dirichlet weighted eigenvalue problem of the elliptic operator in divergence form on compact Riemannian manifolds (M,g,e-ϕdv). We establish a Yang-type inequality of this problem. We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compac...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/387953 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832555060332068864 |
|---|---|
| author | Shenyang Tan Tiren Huang Wenbin Zhang |
| author_facet | Shenyang Tan Tiren Huang Wenbin Zhang |
| author_sort | Shenyang Tan |
| collection | DOAJ |
| description | We investigate the Dirichlet weighted eigenvalue problem of the elliptic operator in divergence form on compact Riemannian manifolds (M,g,e-ϕdv). We establish a Yang-type inequality of this problem. We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below and any complete manifolds admitting eigenmaps to a sphere. |
| format | Article |
| id | doaj-art-95751084d3d0403396dfab02cd0fc6cd |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-95751084d3d0403396dfab02cd0fc6cd2025-02-03T05:49:47ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/387953387953Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian ManifoldsShenyang Tan0Tiren Huang1Wenbin Zhang2Taizhou Institute of Sci. & Tech., NUST., Taizhou 225300, ChinaDepartment of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaTaizhou Institute of Sci. & Tech., NUST., Taizhou 225300, ChinaWe investigate the Dirichlet weighted eigenvalue problem of the elliptic operator in divergence form on compact Riemannian manifolds (M,g,e-ϕdv). We establish a Yang-type inequality of this problem. We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below and any complete manifolds admitting eigenmaps to a sphere.http://dx.doi.org/10.1155/2015/387953 |
| spellingShingle | Shenyang Tan Tiren Huang Wenbin Zhang Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds Advances in Mathematical Physics |
| title | Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds |
| title_full | Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds |
| title_fullStr | Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds |
| title_full_unstemmed | Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds |
| title_short | Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds |
| title_sort | estimates for eigenvalues of the elliptic operator in divergence form on riemannian manifolds |
| url | http://dx.doi.org/10.1155/2015/387953 |
| work_keys_str_mv | AT shenyangtan estimatesforeigenvaluesoftheellipticoperatorindivergenceformonriemannianmanifolds AT tirenhuang estimatesforeigenvaluesoftheellipticoperatorindivergenceformonriemannianmanifolds AT wenbinzhang estimatesforeigenvaluesoftheellipticoperatorindivergenceformonriemannianmanifolds |