Desigualdade de Carleman global para uma Equação da Onda de Transmissão e Aplicação a um Problema Inverso

Abstract

We consider a transmission wave equation in two embedded domains in R2, 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 strongly convex and a1 > a2. As a consequence of this inequality, uniqueness and Lipschitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coeficient from a single time dependent Neumann boundary measurement.