A skin effect approximation for eddy current problems

This paper concerns an interface problem in the plane. It arises in the study of eddy currents in electromagnetic theory as outlined in section two. Let Γ be a simple, closed curve in E 2 with interior Ω − and exterior Ω +. For any χ ∈ C(Ω ±) let χ± denote the limits from Ω ±. Let n be the exterior normal to Γ and write χ n for grad χ · n.