An inverse problem for the magnetic Schr\"{o}dinger operator on Riemannian manifolds from partial boundary data
Analysis of PDEs
2018-10-10 v1
Abstract
We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger 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
Cite
@article{arxiv.1810.03797,
title = {An inverse problem for the magnetic Schr\"{o}dinger operator on Riemannian manifolds from partial boundary data},
author = {Sombuddha Bhattacharyya},
journal= {arXiv preprint arXiv:1810.03797},
year = {2018}
}