Back to Search
Start Over
An inverse problem for the magnetic Schr\'odinger equation in infinite cylindrical domains
- Publication Year :
- 2016
-
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.
- Subjects :
- Mathematics - Analysis of PDEs
35R30, 35Q41
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1605.06599
- Document Type :
- Working Paper