{"paper":{"title":"Dynamics of Optimal Partial Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gonzalo Davila, Young-Heon Kim","submitted_at":"2015-08-11T18:09:40Z","abstract_excerpt":"This paper considers the evolution dynamics of the free boundaries in terms of the change of $m$, the allowed amount of transported mass or the change of $\\lambda$, the transportation cost cap, i.e. the allowed maximum cost for a unit mass to be transported. Focusing on the quadratic cost function, we show H\\\"older and Lipschitz estimates on the speed of the free boundary motion in terms of $m$ and $\\lambda$, respectively. It is also shown that the parameter $m$ is a Lipschitz function of $\\lambda$, which previously was known only to be a continuous increasing function \\cite{Ca-Mc}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02673","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"}