{"paper":{"title":"A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Lorent","submitted_at":"2010-04-13T21:32:28Z","abstract_excerpt":"The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain $\\Omega\\subset R^2$ the functional is $I_{\\epsilon}(u)=1/2\\int_{\\Omega} \\epsilon^{-1}|1-|Du|^2|^2+\\epsilon|D^2 u|^2$ where $u$ belongs to the subset of functions in $W^{2,2}_{0}(\\Omega)$ whose gradient (in the sense of trace) satisfies $Du(x)\\cdot \\eta_x=1$ where $\\eta_x$ is the inward pointing unit normal to $\\partial \\Omega$ at $x$. In Jabin, Otto, Perthame characterized a class "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2274","kind":"arxiv","version":2},"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"}