{"paper":{"title":"The minimizing problem involving p--Laplacian and Hardy--Littlewood--Sobolev upper critical exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haibo Chen, Yu Su","submitted_at":"2018-05-28T15:49:16Z","abstract_excerpt":"In this paper, we study the minimizing problem: $$ S_{p,1,\\alpha,\\mu}:= \\inf_{u\\in W^{1,p}(\\mathbb{R}^{N})\\setminus\\{0\\}} \\frac{ \\int_{\\mathbb{R}^{N}}|\\nabla u|^{p}\\mathrm{d}x -\n\\mu \\int_{\\mathbb{R}^{N}} \\frac{|u|^{p}}{|x|^{p}} \\mathrm{d}x} {\\left( \\int_{\\mathbb{R}^{N}} \\int_{\\mathbb{R}^{N}} \\frac{|u(x)|^{p^{*}_{\\alpha}}|u(y)|^{p^{*}_{\\alpha}}}{|x-y|^{\\alpha}} \\mathrm{d}x \\mathrm{d}y \\right)^{\\frac{p}{2\\cdot p^{*}_{\\alpha}}}}, $$ where $N\\geqslant3$, $p\\in(1,N)$, $\\mu\\in \\left[ 0, \\left( \\frac{N-p}{p} \\right)^{p} \\right)$, $\\alpha\\in(0,N)$ and $p^{*}_{\\alpha}= \\frac{p}{2}\\left(\\frac{2N-\\alpha}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10986","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"}