On boundary value problems for a version of Maxwell equations

Boundary value problem for the system of equations
$$ \operatorname{rot}\vec H-\sigma\vec E=0, \quad \operatorname{rot}\vec E+\mu\vec H=0, $$
(where $\sigma$ and $\mu$ are positive constants) in a domain $\Omega\Subset R^3$ are considered. Boundary conditions are
$$ H_n\big|_{\partial\Omega}=\varphi(x)\big|_{\partial\Omega},\ \ E_n\big|_{\partial\Omega}=f(x)\big|_{\partial\Omega}. $$
The correcntess of the problem is proved if $\partial\Omega$ is smooth. The potential theory is used to get this result.