Stability estimates in inverse problems for the Schr\"odinger and wave equations with trapping
Analysis of PDEs
2022-07-19 v2 Spectral Theory
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.
Keywords
Cite
@article{arxiv.2106.11167,
title = {Stability estimates in inverse problems for the Schr\"odinger and wave equations with trapping},
author = {Victor Arnaiz and Colin Guillarmou},
journal= {arXiv preprint arXiv:2106.11167},
year = {2022}
}
Comments
42 pages, revised version after refereeing. To appear in Revista Matem\'atica Iberoamericana