Stability estimates in inverse problems for the Schrödinger and wave equations with trapping

Abstract

. For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish H¨older type stability estimates in the geometric inverse problem of determining the electric potential or the conformal factor from the Dirichlet-to-Neumann map associated with the Schr¨odinger equation and the wave equation. The novelty in this result lies in the fact that we allow some geodesics to be trapped inside the manifold and have infinite length.