Asymptotics of the s-perimeter as s ↘ 0
Serena Dipierro, Valdinoci, E. · Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano) · 2013
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.