Strong unique continuation property for time harmonic Maxwell equations

Abstract

We give a strong unique continuation theorem for time harmonic Maxwell's equations in inhomogeneous anisotropic media of three dimensional space. The components of the matrices in the constitutive relations are supposed to be Hölder continuous. Furthermore, they are supposed to be differentiable except at one point where they may have critical singularities of Coulomb type. These assumptions prevent us to use the usual second order approach, so that we have to utilize a certain nice structure of Maxwell's equations as the first order system.