On an $H^r(\curl,\O)$ estimate for a Maxwell-type system in convex domains

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.