{"paper":{"title":"Regularity of the Eikonal equation with two vanishing entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Lorent, Guanying Peng","submitted_at":"2016-10-02T08:16:54Z","abstract_excerpt":"The Aviles-Giga functional $I_{\\epsilon}(u)=\\int_{\\Omega} \\frac{\\left|1-\\left|\\nabla u\\right|^2\\right|^2}{\\epsilon}+\\epsilon \\left|\\nabla^2 u\\right|^2 \\, dx$ is a well known second order functional that models phenomena from blistering to liquid crystals. The zero energy states of the Aviles-Giga functional have been characterized by Jabin, Otto, Perthame. Among other results they showed that if $\\lim_{n\\rightarrow \\infty} I_{\\epsilon_n}(u_n)=0$ for some sequence $u_n\\in W^{2,2}_0(\\Omega)$ and $u=\\lim_{n\\rightarrow \\infty} u_n$ then $\\nabla u$ is Lipschitz continuous outside a locally finite s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00237","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"}