The Laplace-Beltrami Operator on the Surface of the Ellipsoid
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is reduced to a two-parameter regular Sturm-Liouville problem i...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212353 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Laplace-Beltrami Operator on the Surface of the Ellipsoid. Hans Volkmer. SIGMA 20 (2024), 067, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862638414764965888 |
|---|---|
| author | Volkmer, Hans |
| author_facet | Volkmer, Hans |
| citation_txt | The Laplace-Beltrami Operator on the Surface of the Ellipsoid. Hans Volkmer. SIGMA 20 (2024), 067, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is reduced to a two-parameter regular Sturm-Liouville problem involving ordinary differential operators. This two-parameter eigenvalue problem has two families of eigencurves whose intersection points determine the eigenvalues of the Laplace-Beltrami operator. Eigenvalues are approximated numerically through eigenvalues of generalized matrix eigenvalue problems. Ellipsoids close to spheres are studied employing Lamé polynomials.
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| first_indexed | 2026-03-15T02:29:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212353 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T02:29:51Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Volkmer, Hans 2026-02-05T09:55:58Z 2024 The Laplace-Beltrami Operator on the Surface of the Ellipsoid. Hans Volkmer. SIGMA 20 (2024), 067, 21 pages 1815-0659 2020 Mathematics Subject Classification: 34B30; 34L15 arXiv:2312.01620 https://nasplib.isofts.kiev.ua/handle/123456789/212353 https://doi.org/10.3842/SIGMA.2024.067 The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is reduced to a two-parameter regular Sturm-Liouville problem involving ordinary differential operators. This two-parameter eigenvalue problem has two families of eigencurves whose intersection points determine the eigenvalues of the Laplace-Beltrami operator. Eigenvalues are approximated numerically through eigenvalues of generalized matrix eigenvalue problems. Ellipsoids close to spheres are studied employing Lamé polynomials. The author thanks the referees whose remarks led to several improvements in the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Laplace-Beltrami Operator on the Surface of the Ellipsoid Article published earlier |
| spellingShingle | The Laplace-Beltrami Operator on the Surface of the Ellipsoid Volkmer, Hans |
| title | The Laplace-Beltrami Operator on the Surface of the Ellipsoid |
| title_full | The Laplace-Beltrami Operator on the Surface of the Ellipsoid |
| title_fullStr | The Laplace-Beltrami Operator on the Surface of the Ellipsoid |
| title_full_unstemmed | The Laplace-Beltrami Operator on the Surface of the Ellipsoid |
| title_short | The Laplace-Beltrami Operator on the Surface of the Ellipsoid |
| title_sort | laplace-beltrami operator on the surface of the ellipsoid |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212353 |
| work_keys_str_mv | AT volkmerhans thelaplacebeltramioperatoronthesurfaceoftheellipsoid AT volkmerhans laplacebeltramioperatoronthesurfaceoftheellipsoid |