{"paper":{"title":"Density estimates for a variational model driven by the Gagliardo norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Ovidiu Savin","submitted_at":"2010-07-13T14:31:04Z","abstract_excerpt":"We prove density estimates for level sets of minimizers of the energy $$\\eps^{2s}\\|u\\|_{H^s(\\Omega)}^2+\\int_\\Omega W(u)\\,dx,$$ with $s \\in (0,1)$, where $\\|u\\|_{H^s(\\Omega)}$ denotes the total contribution from $\\Omega$ in the $H^s$ norm of $u$, and $W$ is a double-well potential.\n  As a consequence we obtain, as $\\eps \\to 0$, the uniform convergence of the level sets of $u$ to either a $H^s$-nonlocal minimal surface if $s\\in(0,\\frac 1 2)$, or to a classical minimal surface if $s \\in[\\frac 1 2,1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2114","kind":"arxiv","version":3},"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"}