Have we got a similar Green identity with the following, $\Omega \subset \mathbb{R}^3$, $E \in H(curl, \Omega)$, $\Phi$ test function smooth enough and scalar, $$ \int_\Omega curl(E)\Phi d\Omega \overset{?}{=} ... $$ Moreover, I'd like to know if the change of coordinate system impacts on Green formula ? Thanks in advance
2026-04-24 01:02:49.1776992569
Green formula, Maxwell
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For a better understanding of the space $H(\operatorname{curl},\Omega)$, I suggest you to take a look in this book page 257. For your second question, after knowing that there is a formula for your expression, try to apply change of variables on it and see what happens.