Sharp estimates for the Neumann functions and applications to quantitative photo-acoustic imaging in inhomogeneous media

Habib Ammari, Hyeonbae Kang, Seick Kim

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6 Citations (Scopus)

Abstract

We obtain sharp L p and Hölder estimates for the Neumann function of the operator ∇;{dot operator}γ∇;-ik on a bounded domain. We also obtain quantitative description of its singularity. We then apply these estimates to quantitative photo-acoustic imaging in inhomogeneous media. The problem is to reconstruct the optical absorption coefficient of a diametrically small anomaly from the absorbed energy density.

Original languageEnglish
Pages (from-to)41-72
Number of pages32
JournalJournal of Differential Equations
Volume253
Issue number1
DOIs
Publication statusPublished - 2012 Jul 1

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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