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

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

2012-04-03

arxiv.org/abs/1204.0750v1

Mathematics

Analysis of PDEs

Scientific paper

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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