Volume 29, 2023
|Number of page(s)||15|
|Published online||11 January 2023|
Asymptotic analysis of a family of non-local functionals on sets
Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia,
via Campi 213,
2 Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy
* Corresponding author: email@example.com
Accepted: 30 November 2022
We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate on more regulars sets. Finally, some examples are discussed.
Mathematics Subject Classification: 49Q15 / 28A75
Key words: Finite perimeter sets / non-local perimeters / anisotropic perimeters
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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