JOURNAL ARTICLE

Lattice tilings minimizing nonlocal perimeters.

  • Published In: Communications in Contemporary Mathematics, 2025, v. 27, n. 6. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Cesaroni, Annalisa; Fragalà, Ilaria; Novaga, Matteo 3 of 3

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. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Communications in Contemporary Mathematics. 2025/08, Vol. 27, Issue 6, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2025
  • ISSN:0219-1997
  • DOI:10.1142/S0219199724500433
  • Accession Number:185394140
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