  In this paper the "strong" Maxwell operator defined on 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 a convex domain, and, more
generally, in a domain, which is locally $(W_3^2 \cap
W^1_\infty)$-diffeomorphic to convex one, the "strong" and the "weak" Maxwell
operators coincide.
