{"paper":{"title":"On the Dirichlet and Neumann evolution operators in R^d_+","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lorenzi, Luciana Angiuli","submitted_at":"2013-07-20T18:16:42Z","abstract_excerpt":"We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators $G_{\\mathcal{D}}(t,s)$ and $G_{\\mathcal{N}}(t,s)$ associated with a class of nonautonomous elliptic operators $\\A(t)$ with unbounded coefficients defined in $I\\times \\Rd_+$ (where $I$ is a right-halfline or $I=\\R$). We also prove the existence and the uniqueness of a tight evolution system of measures $\\{\\mu_t^{\\mathcal{N}}\\}_{t \\in I}$ associated with $G_{\\mathcal{N}}(t,s)$, which turns out to be sub-invariant for $G_{\\mathcal{D}}(t,s)$, and we study the asymptotic behaviour of the evo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5447","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"}