Inverse problem for a nonlocal diffuse optical tomography equation

Abstract

In this article a nonlocal analogue of an inverse problem in diffuse optical tomography is considered. We show that whenever one has given two pairs of diffusion and absorption coefficients $({\gamma }_j,q_j)$, $j=1,2$, such that there holds $q_1=q_2$ in the measurement set $W$ and they generate the same DN data, then they are necessarily equal in ${\mathbb{R}}^n$ and $\Omega$, respectively. Additionally, we show that the condition $q_1{|}_W=q_2{|}_W$ is optimal in the sense that without this restriction one can construct two distinct pairs $({\gamma }_j,q_j)$, $j=1,2$ generating the same DN data.

26 pages, 3 figures

Cited by in corpus (1)

• Calderón problem for fractional Schrödinger operators on closed Riemannian manifolds