Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

Serena  Dipierro; Ovidiu  Savin; Enrico  Valdinoci

doi:10.1007/s12220-018-0045-z

Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

Serena Dipierro, Ovidiu Savin, Enrico Valdinoci

School of Physics, Mathematics and Computing

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1-28
Number of pages	28
Journal	Journal of Geometric Analysis
DOIs	https://doi.org/10.1007/s12220-018-0045-z
Publication status	E-pub ahead of print - 11 Jun 2018

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Nonlocal Equations at Work
Dipierro, S. & Valdinoci, E.
Australian Research Council
30/06/17 → 31/12/21
Project: Research

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abstract = "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.",

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AB - 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.

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Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

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Nonlocal Equations at Work

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