{"paper":{"title":"Optimal Ballistic Transport and Hopf-Lax Formulae on Wasserstein Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nassif Ghoussoub","submitted_at":"2017-05-16T23:08:20Z","abstract_excerpt":"We investigate the optimal mass transport problem associated to the following \"ballistic\" cost functional on phase space $M\\times M^*$, $$ b_T(v, x):=\\inf\\{\\langle v, \\gamma (0)\\rangle +\\int_0^TL(\\gamma (t), {\\dot \\gamma}(t))\\, dt, \\gamma \\in C^1([0, T), M), \\gamma(T)=x\\}, $$ where $M=\\mathbb{R}^d$, $T>0$, and $L:M\\times M \\to \\mathbb{R}$ is a Lagrangian that is jointly convex in both variables. Under suitable conditions on the initial and final probability measures, we use convex duality \\`a la Bolza and Monge-Kantorovich theory to lift classical Hopf-Lax formulae from state space to Wasserst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05951","kind":"arxiv","version":2},"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"}