Laplace operator

In vector calculus, the Laplace operator or Laplacian is a differential operator equal to the sum of all the second partial derivatives of a dependent variable.

This corresponds to div(grad φ), hence the use of the symbol del to represent it:

It is also written as Δ.

In two-dimensional Cartesian coordinates, the Laplacian is:

In three:

It occurs, for example, in Laplace's equation.