Increasing stability for the inverse source problem in electromagnetic waves with conductivity

Abstract

In this paper, we show the stability of the inverse source problem for the Maxwell equations with conductivity. The tangential components of the electric and magnetic fields on the boundary at multiple frequencies are required as the data for the analysis. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases. The explicit dependence of the stability estimate on the constant conductivity is derived. The analysis employs scattering theory to obtain the holomorphic domain and an upper bound for the resolvent of the elliptic operator.