{"paper":{"title":"Summability estimates on transport densities with dirichlet regions on the boundary via symmetrization techniques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OC"],"primary_cat":"math.AP","authors_text":"Filippo Santambrogio (LM-Orsay), Samer Dweik (LM-Orsay)","submitted_at":"2016-06-02T14:44:06Z","abstract_excerpt":"In this paper we consider the mass transportation problem in a bounded domain $\\Omega$ where a positive mass f + in the interior is sent to the boundary $\\partial\\Omega$, appearing for instance in some shape optimization problems, and we prove summability estimates on the associated transport density $\\sigma$, which is the transport density from a diffuse measure to a measure on the boundary f -- = P \\# f + (P being the projection on the boundary), hence singular. Via a symmetrization trick, as soon as $\\Omega$ is convex or satisfies a uniform exterior ball condition, we prove L p estimates (i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00705","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"}