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Ellipsoidal Harmonics by George Dassios

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7Boundary value problems in ellipsoidal geometry

7.1 Expansion of the fundamental solution

Since the ellipsoidal geometry governs natural processes which exhibit directional differentiation, it is obvious that many real-life problems have to be formulated in the framework of the ellipsoidal coordinate system. Furthermore, many problems of scientific and technological interest are postulated as boundary value problems in ellipsoidal domains. Consequently, it is very important to develop systematic techniques to handle these types of problems. Solving boundary value problems in an ellipsoidal environment is much harder than solving problems in a spherical one, and in many instances it is impossible to obtain an analytic solution in closed form. ...

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