{"paper":{"title":"Free boundary regularity in the optimal partial transport problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emanuel Indrei","submitted_at":"2012-10-11T02:59:36Z","abstract_excerpt":"In the optimal partial transport problem, one is asked to transport a fraction $0<m \\leq \\min\\{||f||_{L^1}, ||g||_{L^1}\\}$ of the mass of $f=f \\chi_\\Omega$ onto $g=g\\chi_\\Lambda$ while minimizing a transportation cost. If $f$ and $g$ are bounded away from zero and infinity on strictly convex domains $\\Omega$ and $\\Lambda$, respectively, and if the cost is quadratic, then away from $\\partial(\\Omega \\cap \\Lambda)$ the free boundaries of the active regions are shown to be $C_{loc}^{1,\\alpha}$ hypersurfaces up to a possible singular set. This improves and generalizes a result of Caffarelli and McC"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3111","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"}