{"paper":{"title":"The superposition principle for the continuity equation with singular flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Giuseppe Savar\\'e, Riccarda Rossi, Stefano Almi","submitted_at":"2025-06-18T10:12:49Z","abstract_excerpt":"Representation results for absolutely continuous curves $\\mu:[0,T]\\to \\mathcal{P}_p(\\mathbb{R}^d)$, $p>1$, with values in the Wasserstein space $(\\mathcal{P}_p(\\mathbb{R}^d),W_p)$ of Borel probability measures in $\\mathbb{R}^d$ with finite $p$-moment, provide a crucial tool to study evolutionary PDEs in a measure-theoretic setting. They are strictly related to the superposition principle for measure-valued solutions to the continuity equation. This paper addresses the extension of these results to the case $p=1$, and to curves $\\mu:[0,+\\infty)\\to\\mathcal{P}_1(\\mathbb{R}^d)$ that are only of bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.15333","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.15333/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}