On the computation of Lame functions, of eigenvalues and eigenfunctions of some potential operators

摘要

Eigenvalue problems for the double-layer potential operator and the electrostatic integral operator are of considerable interest in some models Sor permanent magnetization of compact bodies. For the case that the underlying surface is either a sphere; a spheroid or a triaxial ellipsoid, explicit expressions for eigenvalues and eigen functions are well known. For the ellipsoid, these quantities are given in terms for Lame functions and surface ellipsoidal harmonics. Since only few Lame functions can be written in closed form numerical methods are required. We provide an effective scheme for the computation these functions. [References: 14]