{"paper":{"title":"Benamou-Brenier and duality formulas for the entropic cost on $RCD^*(K,N)$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Tamanini, Nicola Gigli","submitted_at":"2018-05-15T16:29:17Z","abstract_excerpt":"In this paper we prove that, within the framework of $RCD^*(K,N)$ spaces with $N < \\infty$, the entropic cost (i.e. the minimal value of the Schr\\\"odinger problem) admits:\n  - a threefold dynamical variational representation, in the spirit of the Benamou-Brenier formula for the Wasserstein distance;\n  - a Hamilton-Jacobi-Bellman dual representation, in line with Bobkov-Gentil-Ledoux and Otto-Villani results on the duality between Hamilton-Jacobi and continuity equation for optimal transport;\n  - a Kantorovich-type duality formula, where the Hopf-Lax semigroup is replaced by a suitable `entropi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06325","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"}