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

Bibliographical note

Funding Information:
✩ This work was supported by the ERC Advanced Grant Project MULTIMOD-267184 and NRF grants Nos. 2009-0090250, 2010-0017532, 2010-0008224, and R31-10049 (WCU program). * Corresponding author. E-mail addresses: habib.ammari@ens.fr (H. Ammari), hbkang@inha.ac.kr (H. Kang), kimseick@yonsei.ac.kr (S. Kim).

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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