The Calderón problem for variable coefficients nonlocal elliptic operators. Issue 12 (2nd December 2017) - Ghosh, Tuhin; Lin, Yi-Hsuan; Xiao, Jingni
ABSTRACT: In this paper, we introduce an inverse problem of a Schrödinger type variable nonlocal elliptic operator (−∇⋅( A ( x )∇)) s + q ), for 0< s <1. We determine the unknown bounded potential q from the exterior partial measurements associated with the nonlocal Dirichlet-to-Neumann map for any dimension n ≥2. Our results generalize the recent initiative [18 ] of introducing and solving inverse problem for fractional Schrödinger operator ((− Δ ) s + q ) for 0< s <1. We also prove some regularity results of the direct problem corresponding to the variable coefficients fractional differential operator and the associated degenerate elliptic operator.