potentiaaliteoriasta
Potentiaaliteoria, also known as potential theory, is a branch of mathematical analysis that studies harmonic functions and their generalizations. A harmonic function is a twice continuously differentiable function that satisfies Laplace’s equation, ∆u = 0, in a given domain. These functions arise naturally as solutions to classical boundary value problems, and they possess several remarkable properties, such as the mean value property and the maximum principle, which allow for deep insights into the behavior of physical and mathematical systems.
The origins of the discipline can be traced back to eighteenth‑century physics, where mathematicians like Legendre
Potential theory merges concepts from several areas of mathematics, including partial differential equations, functional analysis, complex
Applications of potential theory are abundant. In physics, it is used to model electrostatic, gravitation, and