RECONSTRUCTING A POTENTIAL PERTURBATION OF THE BIHARMONIC OPERATOR ON TRANSVERSALLY ANISOTROPIC MANIFOLDS

We prove that a continuous potential q can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the perturbed biharmonic operator Delta(2)(g) + q on a conformally transversally anisotropic Riemannian manifold of dimension >= 3 with boundary, assuming that the geodesic ray transform on the transversal manifold is constructively invertible. This is a constructive counterpart of the uniqueness result of [56]. In particular, our result is applicable and new in the case of smooth bounded domains in the 3-dimensional Euclidean space as well as in the case of 3-dimensional admissible manifolds.