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Second-order asymptotics of the fractional perimeter as s → 1

1 Dipartimento di Scienze Statistiche, Università di Padova, Via Cesare Battisti 241/243, 35121 Padova, Italy
2 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

This contribution is part of the Special Issue: Partial Differential Equations from theory to applications—Dedicated to Alberto Farina, on the occasion of his 50th birthday
Guest Editors: Serena Dipierro; Luca Lombardini
Link: http://www.aimspress.com/newsinfo/1396.html

Special Issues: Partial Differential Equations from theory to applications—Dedicated to Alberto Farina, on the occasion of his 50th birthday

In this note we provide a second-order asymptotic expansion of the fractional perimeter Ps(E), as $s\to 1^-$, in terms of the local perimeter and of a higher order nonlocal functional.
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© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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