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The interface problem describing the scattering of time-harmonicelectromagnetic waves by a dielectric body is often formulated as a pair ofcoupled boundary integral equations for the electric and magnetic currentdensities on the interface $\Gamma$. In this paper, following an idea developedby Kleinman and Martin \cite{KlMa} for acoustic scattering problems, weconsider methods for solving the dielectric scattering problem using a singleintegral equation over $\Gamma$ for a single unknown density. One knows thatsuch boundary integral formulations of the Maxwell equations are not uniquelysolvable when the exterior wave number is an eigenvalue of an associatedinterior Maxwell boundary value problem. We obtain four different families ofintegral equations for which we can show that by choosing some parameters in anappropriate way, they become uniquely solvable for all real frequencies. Weanalyze the well-posedness of the integral equations in the space of finiteenergy on smooth and non-smooth boundaries.

On the Kleinman–Martin Integral Equation Method for Electromagnetic Scattering by a Dielectric Body