{"paper":{"title":"A Trudinger-Moser inequality for conical metric in the unit ball","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xiaobao Zhu, Yunyan Yang","submitted_at":"2018-08-16T00:46:09Z","abstract_excerpt":"In this note, we prove a Trudinger-Moser inequality for conical metric in the unit ball. Precisely, let $\\mathbb{B}$ be the unit ball in $\\mathbb{R}^N$ $(N\\geq 2)$, $p>1$, $g=|x|^{\\frac{2p}{N}\\beta}(dx_1^2+\\cdots+dx_N^2)$ be a conical metric on $\\mathbb{B}$, and $\\lambda_p(\\mathbb{B})=\\inf\\left\\{\\int_\\mathbb{B}|\\nabla u|^Ndx: u\\in W_0^{1,N}(\\mathbb{B}),\\,\\int_\\mathbb{B}|u|^pdx=1\\right\\}$. We prove that for any $\\beta\\geq 0$ and $\\alpha<(1+\\frac{p}{N}\\beta)^{N-1+\\frac{N}{p}}\\lambda_p(\\mathbb{B})$, there exists a constant $C$ such that for all radially symmetric functions $u\\in W_0^{1,N}(\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05316","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"}