{"paper":{"title":"Phase field approach to optimal packing problems and related Cheeger clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Beniamin Bogosel, Dorin Bucur, Ilaria Fragala","submitted_at":"2017-06-17T09:42:02Z","abstract_excerpt":"In a fixed domain of $\\Bbb{R}^N$ we study the asymptotic behaviour of optimal clusters associated to $\\alpha$-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter $\\alpha$ converges to the \"critical\" value $\\Big (\\frac{N-1}{N}\\Big ) _+$, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute $\\alpha$-Cheeger constants, optimal clust"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05506","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}