{"paper":{"title":"Uniform estimates of Landau-de Gennes minimizers in the vanishing elasticity limit with line defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Haotong Fu, Huaijie Wang, Wei Wang","submitted_at":"2025-08-03T15:51:18Z","abstract_excerpt":"For the Landau-de Gennes functional modeling nematic liquid crystals in dimension three, we prove that, if the energy is bounded by $C(\\log\\frac{1}{\\varepsilon}+1)$, then the sequence of minimizers $\\{\\mathbf{Q}_{\\varepsilon}\\}_{\\varepsilon\\in (0,1)}$ is relatively compact in $W_{\\operatorname{loc}}^{1,p}$ for every $1<p<2$. This extends the classical compactness theorem of Bourgain-Br\\'{e}zis-Mironescu [Publ. Math., IH\\'{E}S, 99:1-115, 2004] for complex Ginzburg-Landau minimizers to the $\\mathbb R\\mathbf P^2$-valued Landau-de Gennes setting. Moreover, We obtain local bounds on the integral of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01811","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/2508.01811/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"}