{"paper":{"title":"Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Lunardi, L. Angiuli, L. Lorenzi","submitted_at":"2012-03-06T19:01:24Z","abstract_excerpt":"We consider a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $I\\times\\R^d$, where $I$ is a right-halfline. We prove logarithmic Sobolev and Poincar\\'e inequalities with respect to an associated evolution system of measures $\\{\\mu_t: t \\in I\\}$, and we deduce hypercontractivity and asymptotic behaviour results for the evolution operator $G(t,s)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1280","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"}