Geodesic
On boundary value problems for a version of Maxwell equations
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 29, Tome 264 (2000), pp. 311-320

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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. 
@article{ZNSL_2000_264_a20,
     author = {Sh. Sakhaev},
     title = {On boundary value problems for a version of {Maxwell} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {311--320},
     publisher = {mathdoc},
     volume = {264},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_264_a20/}
}
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Sh. Sakhaev. On boundary value problems for a version of Maxwell equations. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 29, Tome 264 (2000), pp. 311-320. http://geodesic.mathdoc.fr/item/ZNSL_2000_264_a20/