In their renown 2001 paper Bourgain, Brezis and Mironescu studied the limiting behaviour of some nonlocal energies modelled on Gagliardo seminorms. They provided sufficient conditions for the convergence to Sobolev seminorms, and results in the same spirit have been by then proved by several authors. Reversing the point of view, we present necessary conditions and characterize the class of kernels for which nonlocal-to-local formulas hold. The talk is based on joint work with E. Davoli and G. Di Fratta.

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