Second-order asymptotics of the fractional perimeter as <em>s</em> → 1

Annalisa Cesaroni; Matteo Novaga; Annalisa Cesaroni; Matteo Novaga

doi:10.3934/mine.2020023

Mathematics in Engineering

2020, Volume 2, Issue 3: 512-526. doi: 10.3934/mine.2020023

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

Annalisa Cesaroni ^{1
,
,},
Matteo Novaga ²

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

Received: 30 January 2020 Accepted: 13 March 2020 Published: 19 March 2020

In this note we provide a second-order asymptotic expansion of the fractional perimeter P_s(E), as $s\to 1^-$, in terms of the local perimeter and of a higher order nonlocal functional.
- fractional perimeters,
- Γ-convergence,
- second-order expansion
Citation: Annalisa Cesaroni, Matteo Novaga. Second-order asymptotics of the fractional perimeter as s → 1[J]. Mathematics in Engineering, 2020, 2(3): 512-526. doi: 10.3934/mine.2020023

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Abstract

In this note we provide a second-order asymptotic expansion of the fractional perimeter P_s(E), as $s\to 1^-$, in terms of the local perimeter and of a higher order nonlocal functional.

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