Determine a magnetic Schrödinger operator with a bounded magnetic potential from partial data in a slab
type: Item
instance of: scholarly article
title: Determine a magnetic Schrödinger operator with a bounded magnetic potential from partial data in a slab
zbMATH Open document ID: 1469.78016
author: Shitao Liu
author: Yang Yang
published in: Applied Mathematics and Optimization
publication date: 2021-04-22T00:00:00Z
review text: The paper studies inverse boundary value problems with partial data for the following magnetic Schrödinger operator \[ \mathcal{L}_{A,q}(x, D)=\sum_{j=1}^n(D_j+A_j(x))^2+q(x), \] where \(D_j=i^{-1}\frac{\partial}{\partial_{x_j}}\), and a complex-valued magnetic field \(A=(A_j)_{1\le j \le n}\) and an electric potential \(q\) are compactly supported functions in the infinite slab. It is shown that the magnetic field and the electric potential can be uniquely determined when the Dirichlet and Neumann data are given on either different boundary hyperplanes or on the same boundary hyperplanes of the slab. The proof is based on the complex geometric optics solutions constructed in [\textit{K. Krupchyk} et al., Commun Math Phys. 327, 993--1009 (2014; Zbl 1295.35366)], which are special solutions to the magnetic Schrödinger equation with \(L^\infty\) magnetic and electric potentials in a bounded domain.
Mathematics Subject Classification ID: 78A46
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 7336748
zbMATH Keywords: inverse problems
zbMATH Keywords: bounded magnetic potential
zbMATH Keywords: partial data
zbMATH Keywords: slab
reviewed by: D. Kapanadze
MaRDI profile type: Publication
full work available at URL: s00245-018-9537-2
OpenAlex ID: W2898637715
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DOI: 10.1007/S00245-018-9537-2
description: scientific article; zbMATH DE number 7336748