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We show that the knowledge of the Dirichlet–to–Neumann map for a nonlinear magnetic Schrödinger operator on the boundary of a compact complex manifold, equipped with a Kähler metric and admitting sufficiently many global holomorphic functions, determines the nonlinear magnetic and electric potentials uniquely.
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Partial data inverse problems for magnetic Schrödinger operators on conformally transversally anisotropic manifolds
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.
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- Award ID(s):
- 2109199
- PAR ID:
- 10635641
- Publisher / Repository:
- IOS Press
- Date Published:
- Journal Name:
- Asymptotic Analysis
- Volume:
- 140
- Issue:
- 1-2
- ISSN:
- 0921-7134
- Page Range / eLocation ID:
- 25 to 36
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3233/ASY-241909
