{"paper":{"title":"A remark on the radial minimizer of the Ginzburg-Landau functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Brandolini, Francesco Chiacchio","submitted_at":"2013-05-17T09:30:39Z","abstract_excerpt":"Denote by $E_\\epsilon$ the Ginzburg-Landau functional in the plane and let $\\tilde u_\\varepsilon$ be the radial solution to the Euler equation associated to the problem $\\min \\left\\{E_\\varepsilon(u,B_1): \\>\\left. u\\right\\vert _{\\partial B_{1}}=(\\cos \\vartheta,\\sin \\vartheta)\\right\\}$. Let $\\Omega\\subset \\R^2$ be a smooth, bounded domain with the same area as $B_1$. Denoted by $$\\mathcal{K}=\\left\\{v=(v_1,v_2) \\in H^1(\\Omega;\\R^2):\\> \\int_\\Omega v_1\\,dx=\\int_\\Omega v_2\\,dx=0,\\> \\int_\\Omega |v|^2\\,dx\\ge \\int_{B_1} |\\tilde u_\\varepsilon|^2\\,dx\\right\\},$$\n  we prove $$ \\min_{v \\in \\mathcal{K}} E_\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4028","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"}