An inverse problem for the magnetic Schr\"odinger equation in infinite cylindrical domains
Abstract
We study the inverse problem of determining the magnetic field and the electric potential entering the Schr\"odinger equation in an infinite 3D cylindrical domain, by Dirichlet-to-Neumann map. The cylindrical domain we consider is a closed waveguide in the sense that the cross section is a bounded domain of the plane. We prove that the knowledge of the Dirichlet-to-Neumann map determines uniquely, and even H\"older-stably, the magnetic field induced by the magnetic potential and the electric potential. Moreover, if the maximal strength of both the magnetic field and the electric potential, is attained in a fixed bounded subset of the domain, we extend the above results by taking finitely extended boundary observations of the solution, only.
Keywords
Cite
@article{arxiv.1605.06599,
title = {An inverse problem for the magnetic Schr\"odinger equation in infinite cylindrical domains},
author = {Mourad Bellassoued and Yavar Kian and Eric Soccorsi},
journal= {arXiv preprint arXiv:1605.06599},
year = {2016}
}