Green's theorem

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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
ams2001glos-Ge47
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.

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