# Green's theorem

From AMS Glossary

## Green's theorem

A form of the divergence theorem applied to a vector field so chosen as to yield a formula useful in applying the Green's function method of solution of a boundary-value problem.

The most common form of the theorem is where

*dV*and*dS*are elements of the volume*V*and closed bounding surface*S*, respectively; φ and ψ are any twice differential functions with continuous second partial derivatives in*V*;*n*is the outer normal to*S*; and ∇^{2}is the Laplacian operator.