{"paper":{"title":"A sharp Trudinger-Moser inequality on any bounded and convex planar domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Guozhen Lu, Qiaohua Yang","submitted_at":"2015-12-22T17:20:47Z","abstract_excerpt":"Wang and Ye conjectured in [22]:\n  Let $\\Omega$ be a regular, bounded and convex domain in $\\mathbb{R}^{2}$. There exists a finite constant $C({\\Omega})>0$ such that \\[ \\int_{\\Omega}e^{\\frac{4\\pi u^{2}}{H_{d}(u)}}dxdy\\le C(\\Omega),\\;\\;\\forall u\\in C^{\\infty}_{0}(\\Omega), \\] where $H_{d}=\\int_{\\Omega}|\\nabla u|^{2}dxdy-\\frac{1}{4}\\int_{\\Omega}\\frac{u^{2}}{d(z,\\partial\\Omega)^{2}}dxdy$ and $d(z,\\partial\\Omega)=\\min\\limits_{z_{1}\\in\\partial\\Omega}|z-z_{1}|$.}\n  The main purpose of this paper is to confirm that this conjecture indeed holds for any bounded and convex domain in $\\mathbb{R}^{2}$ via "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07163","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"}