Elliptic Regularity Theory Applied to Time Harmonic Anisotropic Maxwell's Equations with Less than Lipschitz Complex Coefficients

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,p}$ for some $ p>3$. Using regularity theory for second order elliptic partial differential equations, we derive $ W^{1,p}$ estimates and Holder estimates for electric and magnetic fields up to the boundary, together with their higher regularity counterparts. We also derive interior estimates in bianisotropic media. [PUBLICATION ABSTRACT]