Calculus of Variations and Geometric Measure Theory

F. Nobili - M. Novaga

Lattice tilings with minimal perimeter and unequal volumes

created by novaga on 19 Jun 2024
modified by nobili on 15 Nov 2024

[BibTeX]

Published Paper

Inserted: 19 jun 2024
Last Updated: 15 nov 2024

Journal: Calc. Var. Partial Differential Equations
Volume: 63
Number: Paper n. 246
Year: 2024
Doi: https://doi.org/10.1007/s00526-024-02871-w

ArXiv: 2406.12461 PDF

Abstract:

We study periodic tessellations of the Euclidean space with unequal cells arising from the minimization of perimeter functionals. Existence results and qualitative properties of minimizers are discussed for different classes of problems, involving local and non-local perimeters. Regularity is then addressed in the general case under volume penalization, and in the planar case with the standard perimeter, prescribing the volumes of each cell. Finally, we show the optimality of hexagonal tilings among partitions with almost equal areas.