The differential operator ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2, in which the symbols x, y, z denote the variables of a rectangular cartesian coordinate system. The laplacian is frequently denoted by the symbol ∇2 (read del square) in accordance with the fact that the laplacian of a scalar function S(x, y, z) is the divergence of the gradient of S, that is, the equation below applies. 
The laplacian operator is involved in some of the most fundamental equations of mathematical physics, namely, Laplace's equation (∇2u = 0), Poisson's equation, various wave equations, and the heat flow and diffusivity equations. See also
