*(English)*Zbl 0805.35154

The author studies an inverse problem for the inhomogeneous Maxwell equations. It is assumed that there exists a bounded set $D\subset {\mathbb{R}}^{3}$ such that outside of $D$ the electric permittivity $\epsilon $ and the magnetic permeability $\mu $ are constant, and that these quantities and the electric conductivity $\sigma $ change discontinuously across $\partial D$ and are inhomogeneous in $D$. It is moreover assumed that $\sigma $ vanishes outside $D$, but is not identically zero inside $D$.

The author proves in a first step that if for two given inhomogeneous media the far field patterns coincide for all incoming plane waves, then the jump discontinuities $\partial {D}_{1}$ and $\partial {D}_{2}$ coincide. Starting from this result, he proves in a second step that under weak conditions also the quantities $\mu ,\epsilon $ and $\sigma $ are uniquely defined by the far field pattern of the solution.

The proof of this second result is based on ideas from the fundamental paper of *J. Sylvester* and *G. Uhlmann* [Ann. Math., II. Ser. 125, 153-169 (1987; Zbl 0625.35078)].