{"paper":{"title":"The Monge-Kantorovich problem for distributions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Giuseppe Buttazzo, Guy Bouchitt\\'e, Luigi De Pascale","submitted_at":"2013-12-19T09:22:54Z","abstract_excerpt":"We study the Kantorovich-Rubinstein transhipment problem when the difference between the source and the target is not anymore a balanced measure but belongs to a suitable subspace $X(\\Omega)$ of first order distribution. A particular subclass $X_0^\\sharp(\\Omega)$ of such distributions will be considered which includes the infinite sums of dipoles $\\sum_k(\\delta_{p_k}-\\delta_{n_k})$ studied in \\cite{P1, P2}. In spite of this weakened regularity, it is shown that an optimal transport density still exists among nonnegative finite measures. Some geometric properties of the Banach spaces $X(\\Omega)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5453","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"}