{"paper":{"title":"Landau-de Gennes model with sextic potentials: asymptotic behavior of minimizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wei Wang, Zhifei Zhang","submitted_at":"2024-03-31T13:04:34Z","abstract_excerpt":"We study a class of Landau-de Gennes energy functionals with a sextic bulk energy density in a three-dimensional domain. We examine the asymptotic behavior of uniformly bounded minimizers in two distinct scenarios: one where their energy remains uniformly bounded, and another where it logarithmically diverges as a function of the elastic constant. In the first case, we show that up to a subsequence, the minimizers converge to a locally minimizing harmonic map in both the $ H_{\\loc}^1 $ and $ C_{\\loc}^j, j\\in \\Z_+ $ norms within compact subsets that are distant from the singularities of the lim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00677","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.00677/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}