{"paper":{"title":"$L^p$-estimates for parabolic systems with unbounded coefficients coupled at zero and first order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego Pallara, Luca Lorenzi, Luciana Angiuli","submitted_at":"2015-05-19T07:15:45Z","abstract_excerpt":"We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space $L^p({\\mathbb R}^d;{\\mathbb R}^m)$, $(d,m \\ge 1)$ with $p\\in [1,+\\infty)$. Sufficient conditions for the associated evolution operator ${\\bf G}(t,s)$ in $C_b({\\mathbb R}^d;{\\mathbb R}^m)$ to extend to a strongly continuous operator in $L^p({\\mathbb R}^d;{\\mathbb R}^m)$ are given. Some $L^p$-$L^q$ estimates are also established together with $L^p$ gradient estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04893","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"}