Second-order asymptotics of the fractional perimeter as $s\to 1$

preprint2020arXivOpen access

In this note we provide a second-order asymptotic expansion of the fractional perimeter Per $_s(E)$ , as $s\to 1^-$ , in terms of the local perimeter and of a higher order nonlocal functional.

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Second-order asymptotics of the fractional perimeter as $s\to 1$

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Second-order asymptotics of the fractional perimeter as s→1s\to 1s→1

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Second-order asymptotics of the fractional perimeter as $s\to 1$