Any real function u(x, y) with continuous second partial derivatives which satisfies Laplace's equation, del ^2 u(x, y) = 0, is called a harmonic function. Harmonic functions are called potential functions in physics and engineering. Potential functions are extremely useful, for example, in electromagnetism, where they reduce the study of a 3-component vector field to a 1-component scalar function. A scalar harmonic function is called a scalar potential, and a vector harmonic function is called a vector potential.

conformal mapping | Dirichlet problem | harmonic analysis | harmonic decomposition | Harnack's inequality | Harnack's principle | Kelvin transformation | Laplace's equation | Poisson integral | Poisson kernel | scalar potential | Schwarz reflection principle | subharmonic function | vector potential