### Abstract

Original language | English |
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Pages (from-to) | 197-214 |

Number of pages | 18 |

Journal | Lecture Notes in Mathematics |

Volume | 2211 |

DOIs | |

Publication status | Published - 2018 |

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**All functions are (Locally) s-Harmonic (up to a small error)—and applications.** / Valdinoci, E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - All functions are (Locally) s-Harmonic (up to a small error)—and applications

AU - Valdinoci, E.

PY - 2018

Y1 - 2018

N2 - The classical and the fractional Laplacians exhibit a number of similarities, but also some rather striking, and sometimes surprising, structural differences. A quite important example of these differences is that any function (regardless of its shape) can be locally approximated by functions with locally vanishing fractional Laplacian, as it was recently proved by Serena Dipierro, Ovidiu Savin and myself. This informal note is an exposition of this result and of some of its consequences.

AB - The classical and the fractional Laplacians exhibit a number of similarities, but also some rather striking, and sometimes surprising, structural differences. A quite important example of these differences is that any function (regardless of its shape) can be locally approximated by functions with locally vanishing fractional Laplacian, as it was recently proved by Serena Dipierro, Ovidiu Savin and myself. This informal note is an exposition of this result and of some of its consequences.

U2 - 10.1007/978-3-319-74042-3_3

DO - 10.1007/978-3-319-74042-3_3

M3 - Article

VL - 2211

SP - 197

EP - 214

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

SN - 0075-8434

ER -