Singular solutions for complex second order elliptic equations and their application to time-harmonic diffuse optical tomography

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Abstract

We construct singular solutions of a complex elliptic equation of second order, having an isolated singularity of any order. In particular, we extend results obtained for the real partial differential equation in divergence form by Alessandrini in 1990. Our solutions can be applied to the determination of the optical properties of an anisotropic medium in time-harmonic Diffuse Optical Tomography (DOT).

Original languageEnglish
Article number109162
JournalApplied Mathematics Letters
Volume157
DOIs
Publication statusPublished - Nov 2024

Keywords

  • Inverse problems
  • Optical tomography
  • Singular solutions

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