Lattice tilings minimizing nonlocal perimeters
| Autor: | Cesaroni, Annalisa, Fragalà, Ilaria, Novaga, Matteo |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S0219199724500433 |
| Popis: | We prove the existence of periodic tessellations of $\mathbb{R}^N$ 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 $\mathbb{R}^N$ , 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. Comment: 19 pages, 2 figures |
| Databáze: | arXiv |
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