Lipschitz stability in an inverse problem for the wave equation

We are interested in the inverse problem of the determination of the potential $p(x),x\in \mathrm{\Omega }\subset {\mathbb{R}}^n$ from the measurement of the normal derivative ${\mathrm{\partial }}_{\nu }u$ on a suitable part ${\mathrm{\Gamma }}_0$ of the boundary of $\mathrm{\Omega }$, where $u$ is the solution of the wave equation ${\mathrm{\partial }}_{tt}u(x,t)-\mathrm{\Delta }u(x,t)+p(x)u(x,t)=0$ set in $\mathrm{\Omega }\times (0,T)$ and given Dirichlet boundary data. More precisely, we will prove local uniqueness and stability for this inverse problem and the main tool will be a global Carleman estimate, result also interesting by itself.