On an elliptic equation arising from photo-acoustic imaging in inhomogeneous media

TL;DR

This paper investigates an elliptic equation from photo-acoustic imaging in inhomogeneous media, establishing regularity and bounds for solutions and Green's functions to improve understanding of imaging in complex media.

Contribution

It proves Holder continuity of weak solutions and derives pointwise bounds for Green's functions in the context of inhomogeneous media, advancing mathematical understanding of photo-acoustic imaging.

Findings

Holder continuity of weak solutions established

Pointwise bounds for Green's functions obtained

Results applicable to Dirichlet and Neumann boundary conditions

Abstract

We study an elliptic equation with measurable coefficients arising from photo-acoustic imaging in inhomogeneous media. We establish Holder continuity of weak solutions and obtain pointwise bounds for Green's functions subject to Dirichlet or Neumann condition.