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: firstname.lastname@example.org
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.