  We propose a possible nonlocal approximation of the Willmore functional, in
the sense of Gamma-convergence, based on the first variation ot the fractional
Allen-Cahn energies, and we prove the corresponding $\Gamma$-limsup estimate.
Our analysis is based on the expansion of the fractional Laplacian in Fermi
coordinates and fine estimates on the decay of higher order derivatives of the
one-dimensional nonlocal optimal profile. This result is the nonlocal
counterpart of that obtained by Bellettini and Paolini, where they proposed a
phase-field approximation of the Willmore functional based on the first
variation of the (local) Allen-Cahn energies.
