Asymptotics of the s-perimeter as s ↘ 0

Serena Dipierro, Alessio Figalli, Giampiero Palatucci, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


We deal with the asymptotic behavior of the s-perimeter of a set E inside a domain Ω as s ↘ 0. 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 Ω Moreover, we construct examples of sets for which the limit does not exist.

Original languageEnglish
Pages (from-to)2777-2790
Number of pages14
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number7
Publication statusPublished - 1 Jul 2013
Externally publishedYes


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