The Calderon problem for variable coefficients nonlocal elliptic operators

In this paper, we introduce an inverse problem of a Schrodinger type variable nonlocal elliptic operator (-delta(A(x)delta))(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 n2. Our results generalize the recent initiative [18] of introducing and solving inverse problem for fractional Schrodinger operator ((-)(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.