A vector Laplacian can be defined for a vector A by del ^2 A = del ( del ·A) - del x( del xA), where the notation ✡ is sometimes used to distinguish the vector Laplacian from the scalar Laplacian del ^2. In tensor notation, A is written A_μ, and the identity becomes del ^2 A_μ | = | (A_(μ;λ))^(;λ) | = | (g^λκ A_(μ;λ))_(;κ) | = | g^λ κ_(;κ) A_(μ;λ) + g^λκ A_(μ;λκ). A tensor Laplacian may be similarly defined.

derivative | Laplacian | tensor Laplacian | vector derivative | vector Poisson equation

Pierre-Simon Laplace