{"paper":{"title":"On continuity equations in infinite dimensions with non-Gaussian reference measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander V. Kolesnikov, Michael R\\\"ockner","submitted_at":"2013-03-28T17:06:09Z","abstract_excerpt":"Let $\\gamma$ be a Gaussian measure on a locally convex space and $H$ be the corresponding Cameron-Martin space. It has been recently shown by L. Ambrosio and A. Figalli that the linear first-order PDE $$ \\dot{\\rho} + \\mbox{div}_{\\gamma} (\\rho \\cdot {b}) =0, \\ \\ \\rho|_{t=0} = \\rho_0, $$ where $\\rho_0 \\cdot \\gamma $ is a probability measure, admits a weak solution, in particular, under the following assumptions: $$ \\|b\\|_{H} \\in L^p(\\gamma), \\ p>1, \\ \\ \\ \\exp\\bigl(\\varepsilon(\\mbox{\\rm div}_{\\gamma} b)_{-} \\bigr) \\in L^1(\\gamma). $$ Applying transportation of measures via triangular maps we prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7184","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"}