%0 Journal Article %J Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 %D 2012 %T Asymptotics of the s-perimeter as s →0 %A Serena Dipierro %A Alessio Figalli %A Giampiero Palatucci %A Enrico Valdinoci %X

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.

%B Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 %I American Institute of Mathematical Sciences %G en %1 7317 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-11T15:55:21Z No. of bitstreams: 1 1204.0750v2.pdf: 216883 bytes, checksum: 3ee8d497a2c0f9a211ec5327e8aa6b9a (MD5) %R 10.3934/dcds.2013.33.2777