Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga

Second-order asymptotics of the fractional perimeter as $s\to 1$

created by cesaroni on 30 Jan 2020
modified by novaga on 20 Mar 2020


Published Paper

Inserted: 30 jan 2020
Last Updated: 20 mar 2020

Journal: Mathematics in Engineering
Volume: 2
Number: 3
Pages: 512-526
Year: 2020

ArXiv: 2001.11415 PDF


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