A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

Abstract

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1>0$ in the inner domain and $a2>0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and $a1>a2$ . As a consequence of this inequality, uniqueness and Lip- schitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement.