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All functions are locally s-harmonic up to a small error
2014, Dipierro, Serena, Savin, Ovidiu, Valdinoci, Enrico
We show that we can approximate every function f Ck (B1) with a s-harmonic function in B1 that vanishes outside a compact set. That is, s-harmonic functions are dense in Ck loc. This result is clearly in contrast with the rigidity of harmonic functions in the classical case and can be viewed as a purely nonlocal feature.
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Local approximation of arbitrary functions by solutions of nonlocal equations
2016, Dipierro, Serena, Savin, Ovidiu, Valdinoci, Enrico
We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally s-caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well.