On the reconstruction of interfaces using complex geometrical optics solutions for the acoustic case

Abstract

We deal with the problem of reconstruction of the coefficient discontinuities (or supports) of scalar divergence form equations with lower order terms from the Dirichlet-to-Neumann map using complex geometrical optics (CGO) solutions. We consider both penetrable and impenetrable obstacles. The usual proofs for justifying this method assume, in addition to the smoothness of the coefficients and the interfaces, the following two conditions.The finiteness of the touching points of the phase’s level curves (or surfaces) of the used CGO solutions with the interface.The positivity of the lower bound of the relative curvature of the interface.In this paper, we show how we can remove these two conditions and justify the reconstruction method considering L∞ coefficients and Lipschitz interfaces of discontinuity.