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arXiv · 1112.2441

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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Abstract

We obtain sharp $L^p$ and H\"older estimates for the Neumann function of the operator $\nabla \cdot \gamma \nabla - ik$ 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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Habib Ammari, Hyeonbae Kang, Seick Kim. 2011-12-12. Sharp estimates for the Neumann functions and applications to quantitative photo-acoustic imaging in inhomogeneous media. https://doi.org/10.1016/j.jde.2012.03.022

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