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In this chapter we look for approximate solutions of Poisson’s equation for regular distributions of matter in the absence of spatial symmetry—a common scenario in fields from astrophysics to electrostatics. This is, classically, approached via series expansions (specifically, the multipole expansion), whose coefficients can be determined by appropriate use of harmonic analysis. Ultimately, this chapter contains the fundamentals of what is generally referred to as “classical potential theory”.

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Classical Potential Theory

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  • 发表日期：

    2026年

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  • Roberto A. Capuzzo Dolcetta

摘要

In this chapter we look for approximate solutions of Poisson’s equation for regular distributions of matter in the absence of spatial symmetry—a common scenario in fields from astrophysics to electrostatics. This is, classically, approached via series expansions (specifically, the multipole expansion), whose coefficients can be determined by appropriate use of harmonic analysis. Ultimately, this chapter contains the fundamentals of what is generally referred to as “classical potential theory”.