| Title | Asymptotics of the s-perimeter as s →0 |
| Publication Type | Journal Article |
| Year of Publication | 2012 |
| Authors | Dipierro, S, Figalli, A, Palatucci, G, Valdinoci, E |
| Journal | Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790 |
| Abstract | 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. |
| DOI | 10.3934/dcds.2013.33.2777 |
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