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.
Asymptotic analysis of a family of non-local functionals on sets / Eleuteri, M; Lussardi, L; Torricelli, A. - In: ESAIM. COCV. - ISSN 1292-8119. - 29:48(2023), pp. 1-15. [10.1051/cocv/2022080]
Asymptotic analysis of a family of non-local functionals on sets
Eleuteri, M;Torricelli, A
2023
Abstract
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.
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