Published Paper

Inserted: 10 apr 2012
Last Updated: 13 aug 2024

Journal: Discrete Contin. Dyn. Syst.
Volume: 33
Number: 7
Pages: 2777-2790
Year: 2013
Doi: doi:10.3934/dcds.2013.33.2777
Links: http://aimsciences.org/journals/pdfs.jsp?paperID=8147&mode=full

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.

Keywords: minimal surfaces, fractional Laplacian, fractional Sobolev spaces, Nonlocal perimeter

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