In this paper, we prove the existence of periodic tessellations of R-N minimizing a general nonlocal perimeter functional, defined as the interaction between a set and its complement through a nonnegative kernel, which we assume to be either integrable at the origin, or singular, with a fractional type singularity. We reformulate the optimal partition problem as an isoperimetric problem among fundamental domains associated with discrete subgroups of R-N, and we provide the existence of a solution by using suitable concentrated compactness type arguments and compactness results for lattices. Finally, we discuss the possible optimality of the hexagonal tessellation in the planar case.
Lattice tilings minimizing nonlocal perimeters
Cesaroni A.;
2024
Abstract
In this paper, we prove the existence of periodic tessellations of R-N minimizing a general nonlocal perimeter functional, defined as the interaction between a set and its complement through a nonnegative kernel, which we assume to be either integrable at the origin, or singular, with a fractional type singularity. We reformulate the optimal partition problem as an isoperimetric problem among fundamental domains associated with discrete subgroups of R-N, and we provide the existence of a solution by using suitable concentrated compactness type arguments and compactness results for lattices. Finally, we discuss the possible optimality of the hexagonal tessellation in the planar case.File | Dimensione | Formato | |
---|---|---|---|
cnfAAM.pdf
embargo fino al 16/10/2025
Descrizione: Author Accepted Manuscript
Tipologia:
Accepted (AAM - Author's Accepted Manuscript)
Licenza:
Creative commons
Dimensione
469.46 kB
Formato
Adobe PDF
|
469.46 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
cesaroni-et-al-2024-lattice-tilings-minimizing-nonlocal-perimeters.pdf
Accesso riservato
Descrizione: VoR
Tipologia:
Published (Publisher's Version of Record)
Licenza:
Accesso privato - non pubblico
Dimensione
419.47 kB
Formato
Adobe PDF
|
419.47 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.