Some inequalities for eigenvalues of an elliptic differential operator
In the present paper, we investigate the eigenvalues of an elliptic differential operator on compact Riemannian manifolds with boundary and derive a general inequality for these eigenvalues. Applying this inequality, we give universal estimates for eigenvalues on compact domains of complete subm...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4429_1c26859bd15de6ed29681a0b82ff7f18.pdf |
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| _version_ | 1841560163895476224 |
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| author | Shahroud Azami Mosayeb Zohrehvand Ghodratallah Fasihi-Ramandi |
| author_facet | Shahroud Azami Mosayeb Zohrehvand Ghodratallah Fasihi-Ramandi |
| author_sort | Shahroud Azami |
| collection | DOAJ |
| description | In the present paper, we investigate the eigenvalues of an elliptic differential operator on compact Riemannian manifolds with boundary and derive a general inequality for these eigenvalues. Applying this inequality, we give universal estimates for eigenvalues on compact domains of complete submanifolds in an Euclidean space, and of complete manifolds admitting special functions. Finally, we find universal bounds on the $(k+1)$-th eigenvalue on such objects in terms of the first $k$ eigenvalues independent of the domains. |
| format | Article |
| id | doaj-art-107cab70e9484a8c8371253518d07c7a |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-107cab70e9484a8c8371253518d07c7a2025-01-04T19:30:18ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052025-01-0114113715410.22103/jmmr.2024.22939.15824429Some inequalities for eigenvalues of an elliptic differential operatorShahroud Azami0Mosayeb Zohrehvand1Ghodratallah Fasihi-Ramandi2Department of Pure Mathematics, Imam Khomeini International University, Qazvin, Iran.Department of mathematics, Malayer University, Malayer, IranDepartment of Pure Mathematics, Imam Khomeini International University, Qazvin, Iran.In the present paper, we investigate the eigenvalues of an elliptic differential operator on compact Riemannian manifolds with boundary and derive a general inequality for these eigenvalues. Applying this inequality, we give universal estimates for eigenvalues on compact domains of complete submanifolds in an Euclidean space, and of complete manifolds admitting special functions. Finally, we find universal bounds on the $(k+1)$-th eigenvalue on such objects in terms of the first $k$ eigenvalues independent of the domains.https://jmmrc.uk.ac.ir/article_4429_1c26859bd15de6ed29681a0b82ff7f18.pdfuniversal boundelliptic operatoreigenvaluesubmanifold |
| spellingShingle | Shahroud Azami Mosayeb Zohrehvand Ghodratallah Fasihi-Ramandi Some inequalities for eigenvalues of an elliptic differential operator Journal of Mahani Mathematical Research universal bound elliptic operator eigenvalue submanifold |
| title | Some inequalities for eigenvalues of an elliptic differential operator |
| title_full | Some inequalities for eigenvalues of an elliptic differential operator |
| title_fullStr | Some inequalities for eigenvalues of an elliptic differential operator |
| title_full_unstemmed | Some inequalities for eigenvalues of an elliptic differential operator |
| title_short | Some inequalities for eigenvalues of an elliptic differential operator |
| title_sort | some inequalities for eigenvalues of an elliptic differential operator |
| topic | universal bound elliptic operator eigenvalue submanifold |
| url | https://jmmrc.uk.ac.ir/article_4429_1c26859bd15de6ed29681a0b82ff7f18.pdf |
| work_keys_str_mv | AT shahroudazami someinequalitiesforeigenvaluesofanellipticdifferentialoperator AT mosayebzohrehvand someinequalitiesforeigenvaluesofanellipticdifferentialoperator AT ghodratallahfasihiramandi someinequalitiesforeigenvaluesofanellipticdifferentialoperator |