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.

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1999-05-25