{"paper":{"title":"The Monge problem with vanishing gradient penalization: Vortices and asymptotic profile","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Filippo Santambrogio (LM-Orsay), Jean Louet (CEREMADE), Luigi De Pascale","submitted_at":"2014-07-25T19:53:58Z","abstract_excerpt":"We investigate the approximation of the Monge problem (minimizing \\int\\_$\\Omega$ |T (x) -- x| d$\\mu$(x) among the vector-valued maps T with prescribed image measure T \\# $\\mu$) by adding a vanishing Dirichlet energy, namely $\\epsilon$ \\int\\_$\\Omega$ |DT |^2. We study the $\\Gamma$-convergence as $\\epsilon$ $\\rightarrow$ 0, proving a density result for Sobolev (or Lipschitz) transport maps in the class of transport plans. In a certain two-dimensional framework that we analyze in details, when no optimal plan is induced by an H ^1 map, we study the selected limit map, which is a new \"special\" Mon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7022","kind":"arxiv","version":3},"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"}