{"paper":{"title":"The Leray--Adams inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Van Hoang Nguyen","submitted_at":"2019-02-28T09:27:19Z","abstract_excerpt":"In this paper, we establish the following Leray--Adams type inequality on a bounded domain $\\Omega$ in $\\mathbb R^{4}$ containing the origin, \\[ \\sup_{u\\in C_0^\\infty(\\Omega), \\tilde I_4[u,\\Omega,R] \\leq 1} \\int_\\Omega \\exp\\left(c\\left( \\frac{|u|}{E_2^{\\beta}\\left(\\frac{|x|}R\\right)}\\right)^2\\right) dx \\leq C |\\Omega| \\] for some constants $c >0$ and $C >0$, where $\\beta\\geq 1$, $R \\geq \\sup_{x\\in \\Omega} |x|$, $ \\tilde I_4[u,\\Omega,R]:= \\int_\\Omega |\\Delta u|^2 dx - \\int_\\Omega \\frac{|u|^2}{|x|^{4} E_1^2\\left(\\frac{|x|}R\\right)} dx, $ and $E_1(t) = 1-\\ln t$, $E_2(t) = \\ln (eE_1(t))$ for $t \\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10970","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"}