Rellich type theorem and unique continuation property for discrete Maxwell operators

Abstract

We study the Rellich type theorem (RT) for the Maxwell operator __ D = D____0 on Z3 in a constant anisotropic medium, i.e., the permittivity and permeability of which are constant non-scalar diagonal matrices. We also prove the unique continuation property (UCP) in the exterior of a compact convex set Kint $\subset$ Z3 for the perturbed Maxwell operator __ Dp = D__p __0 on Z3 for which the permittivity and permeability are locally perturbed from a constant matrix on a compact subset in Kint .