Sharp estimates for the Neumann functions and applications to quantitative photo-acoustic imaging in inhomogeneous media
arXiv:1112.2441 · doi:10.1016/j.jde.2012.03.022
Abstract
We obtain sharp $L^p$ and Hölder estimates for the Neumann function of the operator $\nabla \cdot γ\nabla - ik$ 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.
30 pages