We study the inverse problem of determining the coefficients of the fractional power of a general second order elliptic operator given in the exterior of an open subset of the Euclidean space. We show the problem can be reduced into determining the coefficients from the boundary Cauchy data of the elliptic operator on the open set, the Calder\'{o}n problem. As a corollary we establish several new results for nonlocal inverse problems by using the corresponding results for the local inverse… Expand

Given a fixed α ∈ (0, 1), we study the inverse problem of recovering the isometry class of a smooth closed and connected Riemannian manifold (M, g), given the knowledge of a source-to-solution map… Expand

In this paper we solve the fractional anisotropic Calderón problem on closed Riemannian manifolds of dimensions two and higher. Specifically, we prove that the knowledge of the local… Expand

We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient… Expand