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.
Asymptotics of the $s$-perimeter as $s \searrow 0$ / Serena, Dipierro; Alessio, Figalli; Palatucci, Giampiero; Enrico, Valdinoci. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 33:7(2013), pp. 2777-2790. [10.3934/dcds.2013.33.2777]
Asymptotics of the $s$-perimeter as $s \searrow 0$
PALATUCCI, Giampiero;
2013-01-01
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.File in questo prodotto:
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