{"paper":{"title":"Minimization of a fractional perimeter-Dirichlet integral functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Luis Caffarelli, Ovidiu Savin","submitted_at":"2013-06-22T17:13:00Z","abstract_excerpt":"We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely $$ \\int_\\Om |\\nabla u(x)|^2\\,dx+\\Per\\Big(\\{u > 0\\},\\Om \\Big),$$ with $\\sigma\\in(0,1)$. We obtain regularity results for the minimizers and for their free boundaries $\\p \\{u>0\\}$ using blow-up analysis. We will also give related results about density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5337","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"}