On an inverse problem of determining electromagnetic parameters in Maxwell’s equations from partial boundary measurements

Abstract

In this paper, we deal with an inverse boundary value problem for the Maxwell equations with boundary data assumed known only in accessible part \(\Gamma \) of the boundary. We aim to prove uniqueness results using the Dirichlet to Neumann data with measurements limited to an open part of the boundary and we seek to reconstruct the complex refractive index \({{\varvec{n}}}\) in the interior of a body. Further, using the impedance map restricted to \(\Gamma \), we may identify locations of small volume fraction perturbations of the refractive index.