{"paper":{"title":"Asymptotic behavior of critical points of an energy involving a loop-well potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Itai Shafrir, Petru Mironescu","submitted_at":"2017-06-02T16:06:52Z","abstract_excerpt":"We describe the asymptotic behavior of critical points of $\\int_{\\Omega} [(1/2)|\\nabla u|^2+W(u)/\\varepsilon^2]$ when $\\varepsilon\\to 0$. Here, $W$ is a Ginzburg-Landau type potential, vanishing on a simple closed curve $\\Gamma$. Unlike the case of the standard Ginzburg-Landau potential $W(u)=(1-|u|^2)^2/4$, studied by Bethuel, Brezis and H\\'elein, we do not assume any symmetry on $W$ or $\\Gamma$. In order to overcome the difficulties due to the lack of symmetry, we develop new tools which might be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00737","kind":"arxiv","version":3},"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"}