An inverse problem for the acoustic wave equation with finite sets of boundary data

We study the global stability in determination of multiple coefficients of terms of highest order in an acoustic equation with Dirichlet boundary data. Under regular initial data, we prove the uniqueness and a Hölder stability estimate in the inverse problem with some observations on a suitable subboundary satisfying an appropriate geometrical condition. The key is a Carleman estimate for a hyperbolic operator with variables coefficients.