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
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.