Regularity of electromagnetic fields in convex domains

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.