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

Research output: Contribution to journalArticle

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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 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
Volume19
Issue number4
DOIs
Publication statusPublished - 2017
Externally publishedYes

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Harmonic functions
Harmonic Functions
Harmonic
Compact Set
Rigidity
Clocks
Vanish

Cite this

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title = "All functions are locally s-harmonic up to a small error",
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 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.",
author = "Serena Dipierro and Ovidiu Savin and Enrico Valdinoci",
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All functions are locally s-harmonic up to a small error. / Dipierro, Serena ; Savin, Ovidiu; Valdinoci, Enrico .

In: Journal of the European Mathematical Society, Vol. 19, No. 4, 2017, p. 957-966.

Research output: Contribution to journalArticle

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AB - 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.

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