{"paper":{"title":"A Free Boundary Problem Related to Thermal Insulation: Flat Implies Smooth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dennis Kriventsov","submitted_at":"2015-11-18T20:53:26Z","abstract_excerpt":"We study the regularity of the interface for a new free boundary problem introduced by Caffarelli and Kriventsov. We show that for minimizers of the functional \\[\n  F_1(A,u) = \\int_A |\\nabla u|^2 d\\mathcal{L}^n + \\int_{\\partial A} u^2 + \\bar{C} \\mathcal{L}^n(A) \\] over all pairs $(A,u)$ of open sets $A$ containing a fixed set $\\Omega$ and functions $u\\in H^1(A)$ which equal $1$ on $\\Omega$, the boundary $\\partial A$ locally coincides with the union of the graphs of two $C^{1,\\alpha}$ functions near most points. Specifically, this happens at all points where the interface is trapped between two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05949","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"}