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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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Keywords fractional perimeters; Γ-convergence; second-order expansion

Citation: Annalisa Cesaroni, Matteo Novaga. Second-order asymptotics of the fractional perimeter as s → 1. Mathematics in Engineering, 2020, 2(3): 512-526. doi: 10.3934/mine.2020023


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