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We are interested in the inverse problem of the determination of thepotential $p(x), x\in\Omega\subset\mathbb{R}^n$ from the measurement of thenormal derivative $\partial_\nu u$ on a suitable part $\Gamma_0$ of theboundary of $\Omega$, where $u$ is the solution of the wave equation$\partial_{tt}u(x,t)-\Delta u(x,t)+p(x)u(x,t)=0$ set in $\Omega\times(0,T)$ andgiven Dirichlet boundary data. More precisely, we will prove local uniquenessand stability for this inverse problem and the main tool will be a globalCarleman estimate, result also interesting by itself.

Lipschitz stability in an inverse problem for the wave equation