Partial data for the neumann-dirichlet magnetic Schrödinger inverse problem

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4 Scopus citations

Abstract

We show that an electric potential and magnetic eld can be uniquely determined by partial boundary measurements of the Neumann-to- Dirichlet map of the associated magnetic Schrödinger operator. This improves upon the results in [4] by including the determination of a magnetic eld. The main technical advance is an improvement on the Carleman estimate in [4]. This allows the construction of complex geometrical optics solutions with greater regularity, which are needed to deal with the rst order term in the operator. This improved regularity of CGO solutions may have applications in the study of inverse problems in systems of equations with partial boundary data.

Original languageEnglish
Pages (from-to)959-989
Number of pages31
JournalInverse Problems and Imaging
Volume8
Issue number4
DOIs
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2014 American Institute of Mathematical Sciences.

Keywords

  • Calderón problem
  • Carleman estimate
  • Inverse problems
  • Magnetic Schrödinger equation
  • Partial data
  •  Neumann-Dirichlet map

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

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