A partial data result for the magnetic Schrödinger inverse problem

Chung, Francis

doi:10.2140/apde.2014.7.117

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A partial data result for the magnetic Schrödinger inverse problem

Francis J. Chung

Vol. 7 (2014), No. 1, 117–157

DOI: 10.2140/apde.2014.7.117

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

Vol. 7, No. 1, 2014