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 language | English |
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Pages (from-to) | 41-72 |
Number of pages | 32 |
Journal | Journal of Differential Equations |
Volume | 253 |
Issue number | 1 |
DOIs | |
Publication status | Published - 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