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

Habib Ammari; Hyeonbae Kang; Seick Kim

doi:10.1016/j.jde.2012.03.022

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

Habib Ammari, Hyeonbae Kang, Seick Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 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 language	English
Pages (from-to)	41-72
Number of pages	32
Journal	Journal of Differential Equations
Volume	253
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2012.03.022
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

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10.1016/j.jde.2012.03.022

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abstract = "We obtain sharp L p and H{\"o}lder 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.",

author = "Habib Ammari and Hyeonbae Kang and Seick Kim",

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AU - Ammari, Habib

AU - Kang, Hyeonbae

AU - Kim, Seick

N1 - 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).

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N2 - 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.

AB - 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.

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

Abstract

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