{"paper":{"title":"Higher dimensional Ginzburg-Landau equations under weak anchoring boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changyou Wang, Daniel Phillips, Patricia Bauman","submitted_at":"2017-10-31T12:50:58Z","abstract_excerpt":"For $n\\ge 3$ and $0<\\epsilon\\le 1$, let $\\Omega\\subset\\mathbb R^n$ be a bounded smooth domain and $u_\\epsilon:\\Omega \\subset\\R^n\\to \\mathbb R^2$ solve the Ginzburg-Landau equation under the weak anchoring boundary condition: $$\\begin{cases} -\\Delta u_\\epsilon=\\frac{1}{\\epsilon^2}(1-|u_\\epsilon|^2)u_\\epsilon &\\ {\\rm{in}}\\ \\ \\Omega, \\frac{\\partial u_\\epsilon}{\\partial\\nu}+\\lambda_\\epsilon(u_\\epsilon-g_\\epsilon)=0 & \\ {\\rm{on}}\\ \\ \\partial\\Omega, \\end{cases} $$ where the anchoring strength parameter $\\lambda_\\epsilon=K\\epsilon^{-\\alpha}$ for some $K>0$ and $\\alpha\\in [0,1)$, and $g_\\epsilon\\in C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11437","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"}