Lipschitz stability for the electrical impedance tomography problem: The complex case

Elena Beretta, Elisa Francini

Research output: Contribution to journalArticle

Abstract

where γ is a complex valued L coefficient, satisfying a strong ellipticity condition. In electrical impedance tomography, γ represents the admittance of a conducting body. An interesting issue is the one of determining γ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map {n-ary logical and}γ. Under the above general assumptions this problem is an open issue. In this article we prove that, if we assume a priori that γ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of γ from {n-ary logical and}γ holds.

Original languageEnglish (US)
Pages (from-to)1723-1749
Number of pages27
JournalCommunications in Partial Differential Equations
Volume36
Issue number10
DOIs
StatePublished - Oct 1 2011

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Lipschitz Stability
Dirichlet-to-Neumann Map
Electrical Impedance Tomography
Lipschitz Continuity
Acoustic impedance
Ellipticity
Tomography
Unknown
Coefficient
Knowledge

Keywords

  • Inverse admittivity problem
  • Lipschitz continuous dependence

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Lipschitz stability for the electrical impedance tomography problem : The complex case. / Beretta, Elena; Francini, Elisa.

In: Communications in Partial Differential Equations, Vol. 36, No. 10, 01.10.2011, p. 1723-1749.

Research output: Contribution to journalArticle

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