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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Spherical Potential Theory: Tools and Applications
verfasst von : Christian Gerhards
Erschienen in: Handbook of Mathematical Geodesy
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In the current chapter, we transfer classical potential theoretic concepts from the Euclidean space $$\mathbb{R}^3$$ to a setting intrinsic on the sphere. We present uniqueness results for the Poisson equation on the sphere, explicitly construct Green functions for spherical caps and complete function systems for harmonic approximation, and elaborate on decompositions of vector fields on the sphere. Among the intended applications are problems from oceanography, geodesy, and geomagnetism. Some examples are presented at the end.