{"paper":{"title":"The equation div$u$+$\\langle a, u \\rangle=f$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gyula Csat\\'o, Pierre Bousquet","submitted_at":"2019-01-17T13:38:16Z","abstract_excerpt":"We study the solutions $u$ to the equation $$ \\begin{cases} \\operatorname{div} u + \\langle a , u \\rangle = f & \\textrm{ in } \\Omega,\\\\ u=0 & \\textrm{ on } \\partial \\Omega, \\end{cases} $$ where $a$ and $f$ are given. We significantly improve the existence results of [Csat\\'o and Dacorogna, A Dirichlet problem involving the divergence operator, \\textit{Ann. Inst. H. Poincar\\'e Anal. Non Lin\\'eaire}, 33 (2016), 829--848], where this equation has been considered for the first time. In particular, we prove the existence of a solution under essentially sharp regularity assumptions on the coefficient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05783","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"}