The Calderón problem for variable coefficients nonlocal elliptic operators

Abstract

ABSTRACTIn 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.