H{\"o}lder stability in determining the potential and the damping coefficient in a wave equation

We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an initial-to-boundary operator. We partially modify the arguments in [3] to show that actually we have H{\"o}lder stability instead of logarithmic stability.