TY - JOUR T1 - Asymptotics of the s-perimeter as s →0 JF - Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 Y1 - 2012 A1 - Serena Dipierro A1 - Alessio Figalli A1 - Giampiero Palatucci A1 - Enrico Valdinoci AB -

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.

PB - American Institute of Mathematical Sciences U1 - 7317 U2 - Mathematics U4 - -1 ER -