Asymptotics of the $s$-perimeter as $s\searrow 0$

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Dipierro, Serena; Figalli, Alessio; Palatucci, Giampiero; Valdinoci, Enrico;
(2012)
  • Subject: Mathematics - Analysis of PDEs

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 $... View more
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