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We relate the (anisotropic) variable coefficient local and nonlocalCalder\'on problems by means of the Caffarelli-Silvestre extension. Inparticular, we prove that (partial) Dirichlet-to-Neumann data for thefractional Calder\'on problem in three and higher dimensions determine the(full) Dirichlet-to-Neumann data for the local Calder\'on problem. As aconsequence, any (variable coefficient) uniqueness result for the local problemalso implies a uniqueness result for the nonlocal problem. Moreover, ourapproach is constructive and associated Tikhonov regularization schemes can beused to recover the data. Finally, we highlight obstructions for reversing thisprocedure, which essentially consist of two one-dimensional averagingprocesses.

A Reduction of the Fractional Calder\'on Problem to the Local Calder\'on Problem by Means of the Caffarelli-Silvestre Extension