| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 1 | |
| Number of page(s) | 15 | |
| DOI | https://doi.org/10.1051/cocv/2022080 | |
| Published online | 11 January 2023 | |
Asymptotic analysis of a family of non-local functionals on sets
1
Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia,
via Campi 213,
41125
Modena,
Italy
2
Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino,
c.so Duca degli Abruzzi 24,
10129
Torino,
Italy
* Corresponding author: luca.lussardi@polito.it
Received:
11
October
2021
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
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