Classical potential theory

Classical potential theory studies how scalar fields, like gravitational or electrostatic potentials, behave in space. It explores solutions to equations such as Laplace's equation, which describe how potential functions change and spread out, especially in the absence of sources or sinks. The theory helps us understand phenomena like how electrical or gravitational forces distribute around objects. It uses mathematical tools to analyze properties like harmonic functions, which remain stable and smooth, offering insights into fields' behavior in different environments and informing practical applications in physics and engineering.