The partial differential equation ${\nabla }^{2}V=\frac{{\partial }^{2}V}{\partial x^2}+\frac{{\partial }^{2}V}{\partial y^2}+\frac{{\partial }^{2}V}{\partial z^2}=0$ where ∇² = ∇∙∇ = div grad is the Laplacian differential operator. This equation is important in potential theory. The inhomogeneous version of Laplace’s equation, ∇²V = f, is called Poisson’s equation.