Green's identities are a set of three vector derivative/integral identities which can be derived starting with the vector
derivative identities
(1) |
(2) |
(3) |
(4) |
Subtracting (2) from (1),
(5) |
(6) |
Let have continuous first Partial Derivatives and be Harmonic
inside the region of integration. Then Green's third identity is
(7) |
References
Kaplan, W. Advanced Calculus, 4th ed. Reading, MA: Addison-Wesley, 1991.