  The focus of this paper is the study of the regularity properties of the time
harmonic Maxwell's equations with anisotropic complex coefficients, in a
bounded domain with $C^{1,1}$ boundary. We assume that at least one of the
material parameters is $W^{1,3+\delta}$ for some $\delta>0$. Using regularity
theory for second order elliptic partial differential equations, we derive
$W^{1,p}$ estimates and H\"older estimates for electric and magnetic fields up
to the boundary. We also derive interior estimates in bi-anisotropic media.

Analysis of PDEs