Fr.: équation de Laplace
A → linear differential equation of the second order the solutions of which are important in many fields of science, mainly in electromagnetism, fluid dynamics, and is often used in astronomy. It is expressed by: ∂2V/ ∂x2 + ∂2V/ ∂y2 + ∂2V/ ∂z2 = 0. Laplace's equation can more concisely expressed by: ∇2V = 0. The function V may, for example, be the potential at any point in the electric field where there is no free charge. The general theory of solutions to Laplace's equation is known as potential theory.