Calculus of Variations and Geometric Measure Theory
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Up to a small error, all functions are s-harmonic

Serena Dipierro

created by gelli on 13 Dec 2016
modified on 05 Jan 2017

19 jan 2017 -- 17:00   [open in google calendar]

Aula Seminari Dipartimento di Matematica di Pisa

Abstract.

We would like to present a series of structural results on nonlocal operators. First of all, we will show that "all functions are s-harmonic, up to a small error", namely that any smooth function can be locally approximated by functions whose fractional Laplacian vanishes.

This phenomenon is indeed very general and robust, since related approximation results hold true for all linear nonlocal operators. In particular, no particular structure (such as ellipticity, parabolicity or hyperbolicity) is needed to obtain these density results.

In addition, we show that it is possible to make sense of the fractional Laplacian also for functions with a polynomial growth at infinity, and that the density results are stable with respect to this extended notion.

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