On Hr(curl,Ω) estimates for a Maxwell type system in convex domains

Abstract

In bounded convex domains, the regularity of a vector field u with its divu, curlu in Lr space and the tangential component or the normal component of u over the boundary in Lr space, is established for 1<r<∞. As an application, we derive an Hr(curl,Ω) estimate for solutions to a Maxwell type system with an inhomogeneous boundary condition in convex domains. In contrast to the well-posed region of r in the space Hr(curl,Ω) for the Maxwell type system in Lipschitz domains given by Kar and Sini (2016) [16], we extend the well-posed region to be optimal.