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Zbl 0908.31002
Ritter, S.
On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators. (English)
[J] ZAMM, Z. Angew. Math. Mech. 78, No.1, 66-72 (1998). ISSN 0044-2267; ISSN 1521-4001/e

The author studies in an interesting way two eigenvalue problems for the double-layer potential operator and the electrostatic integral operator. This study is based on ellipsoidal coordinates, Lamé functions of first and second kind and of surface ellipsoidal harmonics. An effective numerical computation of Lamé functions is discussed with applications to eigenvalues of the electrostatic operator. A further study is needed to extend the ideas for the numerical computation of surface ellipsoidal wave functions, which are important for scattering problems involving ellipsoids.
[L.Debnath (Orlando)]

MSC 2000:: *31B10 Integral representations of harmonic functions (higher-dimensional)
33E10 Spheroidal wave functions, etc.
35Q60 PDE of electromagnetic theory and optics
78A30 Electro- and magnetostatics

Keywords: eigenvalue problems; double-layer potential operator; electrostatic integral operator; Lamé functions; ellipsoidal harmonics; numerical computation of Lamé functions

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