We show that we can approximate every function f ∈ Ck (B1) by an s-harmonic function in B1 that vanishes outside a compact set. That is, s-harmonic functions are dense in Cloc k. 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.
All functions are locally $s$-harmonic up to a small error / S. Dipierro, O. Savin, E. Valdinoci. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 19:4(2017), pp. 957-966. [10.4171/JEMS/684]
All functions are locally $s$-harmonic up to a small error
S. DipierroPrimo
;E. ValdinociUltimo
2017
Abstract
We show that we can approximate every function f ∈ Ck (B1) by an s-harmonic function in B1 that vanishes outside a compact set. That is, s-harmonic functions are dense in Cloc k. 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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