All functions are locally s-harmonic up to a small error

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45 Citations (Scopus)


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 Clock. 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.
Original languageEnglish
Pages (from-to)957-966
Number of pages10
JournalJournal of the European Mathematical Society
Issue number4
Publication statusPublished - 2017
Externally publishedYes


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