Reconstructing a potential perturbation of the biharmonic operator on transversally anisotropic manifolds

Abstract

We prove that a continuous potential \begin{document}$ q $\end{document} can be constructively determined from the knowledge of the Dirichlet–to–Neumann map for the perturbed biharmonic operator \begin{document}$ \Delta_g^2+q $\end{document} on a conformally transversally anisotropic Riemannian manifold of dimension \begin{document}$ \ge 3 $\end{document} with boundary, assuming that the geodesic ray transform on the transversal manifold is constructively invertible. This is a constructive counterpart of the uniqueness result of [56]. In particular, our result is applicable and new in the case of smooth bounded domains in the \begin{document}$ 3 $\end{document}–dimensional Euclidean space as well as in the case of \begin{document}$ 3 $\end{document}–dimensional admissible manifolds.