Lattice tilings with minimal perimeter and unequal volumes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909226796843008 |
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| author | Nobili, Francesco Novaga, Matteo |
| author_facet | Nobili, Francesco Novaga, Matteo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12461 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lattice tilings with minimal perimeter and unequal volumes Nobili, Francesco Novaga, Matteo Analysis of PDEs Differential Geometry Functional Analysis 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. |
| title | Lattice tilings with minimal perimeter and unequal volumes |
| topic | Analysis of PDEs Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2406.12461 |