On the stability of an inverse problem for the wave equation

Consider the inverse problem of determining the potential q from the Neumann to Dirichlet map Λ q of the wave equation u tt − Δ u + qu = 0 in Ω × (0, T ) with u ( x , 0) = u t ( x , 0) = 0. In this paper, a nearly Lipschitz-type stability estimate is established for the inverse problem: for any small > 0, there exists β 0 > 0 such that when for some β > β 0 . Here, represents the operator norm.