(adsbygoogle = window.adsbygoogle || []).push({}); As required by the Green's identity, the integrated function has to be smooth and continuous in the integration region Ω.

How about if the function is just discontinuous at the boundary? Actually, this function is an electric field. So its tangential component is naturally continuous, but the normal component is discontinuous due to the abrupt change of refractive index in these two regions. However, a boundary condition is hold that is

## n_1 E_{n1} = n2 E_{n2}##

In this case, can I still use the Green's first identity to the normal component, by treating the integration region as an open region?

If I can, what kind of surface divergence I should use at the boundary?

Thanks for your help

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Green's first identity at the boundary

Loading...

Similar Threads - Green's identity boundary | Date |
---|---|

I What do Stokes' and Green's theorems represent? | Today at 11:26 AM |

A Angular Moment Operator Vector Identity Question | Feb 10, 2018 |

I Green's theorem and Line Integrals | Jul 21, 2016 |

A nasty integral to compute | Jan 20, 2016 |

Differentiating Integral with Green's function | Nov 19, 2015 |

**Physics Forums - The Fusion of Science and Community**