2024/06/18 by Francesco Nobili, Nobili, Francesco, Matteo Novaga +1 · 1 citation
Engineering · Materials Science · #Advanced Materials and Mechanics #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Quasicrystal Structures and Properties #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2406.12461
openalex publication_date 2024/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.