{"paper":{"title":"On the estimates of the derivatives of solutions to nonautonomous Kolmogorov equations and their consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lorenzi, Luciana Angiuli","submitted_at":"2017-02-08T13:54:30Z","abstract_excerpt":"We consider evolution operators $G(t,s)$ associated to a class of nonautonomous elliptic operators with unbounded coefficients, in the space of bounded and continuous functions over $\\mathbb{R}^d$. We prove some new pointwise estimates for the spatial derivatives of the function $G(t,s)f$, when $f$ is bounded and continuous or much smoother. We then use these estimates to prove smoothing effects of the evolution operator in $L^p$-spaces. Finally, we show how pointwise gradient estimates have been used in the literature to study the asymptotic behaviour of the evolution operator and to prove su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02428","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"}