Abstract

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 Hölder estimates for electric and magnetic fields up to the boundary, together with their higher regularity counterparts. We also derive interior estimates in bianisotropic media.

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