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2014 A partial data result for the magnetic Schrödinger inverse problem
Francis Chung
Anal. PDE 7(1): 117-157 (2014). 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.

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Francis Chung. "A partial data result for the magnetic Schrödinger inverse problem." Anal. PDE 7 (1) 117 - 157, 2014. https://doi.org/10.2140/apde.2014.7.117

Information

Received: 22 May 2012; Revised: 20 June 2013; Accepted: 22 August 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1293.35362
MathSciNet: MR3219502
Digital Object Identifier: 10.2140/apde.2014.7.117

Subjects:
Primary: 35R30
Secondary: 35S99

Keywords: Carleman estimate , Dirichlet–Neumann map , Inverse problems , magnetic Schrödinger operator , partial data , pseudodifferential operators , semiclassical analysis

Rights: Copyright © 2014 Mathematical Sciences Publishers

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