A partial data result for the magnetic Schrödinger inverse problem

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18 Scopus citations

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.

Original languageEnglish
Pages (from-to)117-157
Number of pages41
JournalAnalysis and PDE
Volume7
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Carleman estimate
  • Dirichlet-Neumann map
  • Inverse problems
  • Magnetic schrödinger operator
  • Partial data
  • Pseudodifferential operators
  • Semiclassical analysis

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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