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arXiv · 1204.0750

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

Serena Dipierro·Alessio Figalli·Giampiero Palatucci·Enrico Valdinoci
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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.

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Serena Dipierro, Alessio Figalli, Giampiero Palatucci, Enrico Valdinoci. 2012-04-03. Asymptotics of the $s$-perimeter as $s\searrow 0$. https://arxiv.org/abs/1204.0750

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