{"paper":{"title":"Weak regularity of Gauss mass transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Alexander V. Kolesnikov","submitted_at":"2009-04-12T11:39:57Z","abstract_excerpt":"Given two probability measures $\\mu$ and $\\nu$ we consider a mass transportation mapping $T$ satisfying 1) $T$ sends $\\mu$ to $\\nu$, 2) $T$ has the form $T = \\phi \\frac{\\nabla \\phi}{|\\nabla \\phi|}$, where $\\phi$ is a function with convex sublevel sets.\n  We prove a change of variables formula for $T$. We also establish Sobolev estimates for $\\phi$, and a new form of the parabolic maximum principle.\n  In addition, we discuss relations to the Monge-Kantorovich problem, curvature flows theory, and parabolic nonlinear PDE's."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1852","kind":"arxiv","version":4},"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"}