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Asymptotics of the s-perimeter as s →0

TitleAsymptotics of the s-perimeter as s →0
Publication TypeJournal Article
Year of Publication2012
AuthorsDipierro, S, Figalli, A, Palatucci, G, Valdinoci, E
JournalDiscrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790

We deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.


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