  In bounded convex domains, the regularity estimates of a vector field $\u$
with its $\dv\u$, $\curl\u$ in $L^r$ space and the tangential components or the
normal component of $\u$ over the boundary in $L^r$ space, are established for
$1<r<\infty$. As an application, we derive an $H^r(\curl,\O)$ estimate for
solutions to a Maxwell-type system with an inhomogeneous boundary condition in
convex domains.
