{"paper":{"title":"Lack of regularity of the transport density in the monge problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Samer Dweik (LM-Orsay)","submitted_at":"2017-04-24T12:40:38Z","abstract_excerpt":"In this paper, we provide a family of counterexamples to the regularity of the transport density in the classical Monge-Kantorovich problem. We prove that the W^{1,p} regularity of the source and target measures f ^\\pm does not imply that the transport density $\\sigma$ is W^{1,p} , that the BV regularity of f ^\\pm does not imply that $\\sigma$ is BV and that f^\\pm $\\in$ C^\\infty does not imply that $\\sigma$ is W^{1,p} , for large p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07180","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"}