Geodesic
Regularity of electromagnetic fields in convex domains
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 55-85

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The “strong” Maxwell operator defined on the fields from the Sobolev space $W_2^1$, and the “weak” Maxwell operator defined on the natural domain are considered. It is shown, that in the convex domains, and more generally, in the domains which are locally $(W^2_3\cap W^1_\infty)$-diffeomorphic to convex ones, the “strong” and the “weak” Maxwell operators coincide. 
@article{ZNSL_2014_425_a4,
     author = {A. Prohorov and N. Filonov},
     title = {Regularity of electromagnetic fields in convex domains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {55--85},
     publisher = {mathdoc},
     volume = {425},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a4/}
}
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A. Prohorov; N. Filonov. Regularity of electromagnetic fields in convex domains. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 55-85. http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a4/