Coercivity and the Calderon Operator on an Unbounded Domain

Detection of metallic objects in soil lead to the mathematical model of Maxwell's equations in a two-layered space. The full space problem is reduced to a weak formulation for a half-space with a non-local boundary condition using the exterior Calderon operator. For non-dissipative media the Calderon operator exhibits singular spectral properties at the infinite boundary plane. Using weighted Sobolev spaces the weak formulation is uniquely solvable by generalized coercivity conditions.