Stable determination at the boundary of the optical properties of a medium: The static case

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Abstract

The problem of the stable determination of the coefficients of second order elliptic partial differential equations arising in inverse problems is considered. Results of uniqueness and stability at the boundary were obtained in [3] and extended in [8, 9] for the conductivity equation. The common features of these papers are the employment of the singular solutions and the monotonicity assumption introduced in [3]. We revisit the techniques adopted in these papers to stably determine the absorption coefficient in anisotropic media by means of Optical Tomography (OT) in the so-called static case. This also shows that the monotonicity assumption is realistic at least in the context of OT.

Original languageEnglish
Pages (from-to)407-431
Number of pages25
JournalRendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume48
Issue number1
DOIs
Publication statusPublished - 2016

Keywords

  • EIT
  • OT
  • Stability at the boundary

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