{"paper":{"title":"An elementary proof of the continuity from $L_0^2(\\Omega)$ to $H^1_0(\\Omega)^n$ of Bogovskii's right inverse of the divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ricardo G. Duran","submitted_at":"2011-03-18T21:27:03Z","abstract_excerpt":"The existence of right inverses of the divergence as an operator form $H^1_0(\\Omega)^n$ to $L_0^2(\\Omega)$ is a problem that has been widely studied because of its importance in the analysis of the classic equations of fluid dynamics. When $\\Omega$ is a bounded domain which is star-shaped with respect to a ball $B$, a right inverse given by an integral operator was introduced by Bogovskii, who also proved the continuity using the Calder\\'on-Zygmund theory of singular integrals.\n  In this paper we give an alternative elementary proof using the Fourier transform. As a consequence, we obtain esti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3718","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"}