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

Abstract

We obtain sharp $L^p$ and Hölder 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.

30 pages

References in corpus (2)

• The Green function estimates for strongly elliptic systems of second order
• Neumann functions for second order elliptic systems with measurable coefficients

Cited by in corpus (3)

• A global stability estimate for the photo-acoustic inverse problem in layered media
• On an elliptic equation arising from photo-acoustic imaging in inhomogeneous media
• The Concept of Heterogeneous Scattering Coefficients and Its Application in Inverse Medium Scattering