  We deal with the problem of reconstructing interfaces using complex
geometrical optics solutions for the Maxwell system. The contributions are
twofold. First, we justify the enclosure method for the impenetrable obstacle
case avoiding any assumption on the directions of the phases of the CGO's (or
the curvature of obstacle's surface). In addition, we need only a Lipschitz
regularity of this surface. The analysis is based on some fine properties of
the corresponding layer potentials in appropriate Sobolev spaces. Second, we
justify this method also for the penetrable case, where the interface is
modeled by the jump (or the discontinuity) of the magnetic permeability $\mu$.
A key point of the analysis is the global $L^p$-estimates for the curl of the
solutions of the Maxwell system with discontinuous coefficients. These
estimates are justified here for $p$ near $2$ generalizing to the Maxwell's
case the well known Meyers's $L^p$ estimates of the gradient of the solution of
scalar divergence form elliptic problems.
