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June 2018, 12(3): 801-830. doi: 10.3934/ipi.2018034
An inverse problem for the magnetic Schrödinger operator on Riemannian manifolds from partial boundary data
Sombuddha Bhattacharyya
Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore, India
Received September 2016 Revised January 2018 Published March 2018
We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schrödinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the boundary. The uniqueness proof relies on proving a suitable Carleman estimate for functions which vanish only on a part of boundary and constructing complex geometric optics solutions which vanish on a part of the boundary.
Keywords: Differential geometry, inverse problems, Calderón problem, geometric analysis, partial differential equations.
Mathematics Subject Classification: Primary: 58F15, 31B20; Secondary: 35J25.
Citation: Sombuddha Bhattacharyya. An inverse problem for the magnetic Schrödinger operator on Riemannian manifolds from partial boundary data. Inverse Problems & Imaging, 2018, 12 (3) : 801-830. doi: 10.3934/ipi.2018034
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