Vol. 7, No. 1, 2014

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
A partial data result for the magnetic Schrödinger inverse problem

Francis J. Chung

Vol. 7 (2014), No. 1, 117–157
Abstract

This article shows that restricting the domain of the Dirichlet–Neumann map to functions supported on a certain part of the boundary, and measuring the output on, roughly speaking, the rest of the boundary, uniquely determines a magnetic Schrödinger operator. If the domain is strongly convex, either the subset on which the Dirichlet–Neumann map is measured or the subset on which the input functions have support may be made arbitrarily small. The key element of the proof is the modification of a Carleman estimate for the magnetic Schrödinger operator using operators similar to pseudodifferential operators.

Keywords
inverse problems, partial data, Dirichlet–Neumann map, Carleman estimate, magnetic Schrödinger operator, semiclassical analysis, pseudodifferential operators
Mathematical Subject Classification 2010
Primary: 35R30
Secondary: 35S99
Milestones
Received: 22 May 2012
Revised: 20 June 2013
Accepted: 22 August 2013
Published: 7 May 2014
Authors
Francis J. Chung
Department of Mathematics
University of Chicago
Chicago, IL 60637
United States