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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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