Partial data inverse problems for magnetic Schrödinger operators on conformally transversally anisotropic manifolds

Article type: Research Article

Authors: Selim, Salem^{a; *} | Yan, Lili^b

Affiliations: [a] Department of Mathematics, University of California, Irvine, CA 92697-3875, USA | [b] School of Mathematics, University of Minnesota, MN 55455, USA

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We study inverse boundary problems for the magnetic Schrödinger operator with Hölder continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n⩾3 with connected boundary. A global uniqueness result is established for magnetic fields and electric potentials from the partial Cauchy data on the boundary of the manifold provided that the geodesic X-ray transform on the transversal manifold is injective.

Keywords: Inverse problems, magnetic Schrödinger operator, partial data, CTA manifold

DOI: 10.3233/ASY-241909

Journal: Asymptotic Analysis, vol. 140, no. 1-2, pp. 25-36, 2024