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

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

2011-12-12

arxiv.org/abs/1112.2441v1

Journal of Differential Equations 253 (2012) pp. 41-72

Mathematics

Analysis of PDEs

30 pages

Scientific paper

10.1016/j.jde.2012.03.022

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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