# Green's first identity at the boundary

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1. Jan 10, 2016

### Jeffrey Yang

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

2. Jan 16, 2016

### Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

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