The Laplace-Beltrami Operator on the Surface of the Ellipsoid

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Volkmer, Hans
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212353
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Laplace-Beltrami Operator on the Surface of the Ellipsoid. Hans Volkmer. SIGMA 20 (2024), 067, 21 pages

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...