In mathematics, a partial differential equation whose solutions (harmonic functions) are useful in investigating physical problems in three dimensions involving gravitational, electrical, and magnetic fields, and certain types of fluid motion.
Named for Pierre-Simon Laplace , the equation states that the sum of the second partial derivatives (the Laplace operator, or Laplacian) of an unknown function is zero. It can apply to functions of two or three variables, and can be written in terms of a differential operator as Δ F = 0, where Δ is the Laplace operator.