{"paper":{"title":"Pointwise Bounds and Blow-up for Choquard-Pekar Inequalities at an Isolated Singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marius Ghergu, Steven D. Taliaferro","submitted_at":"2015-12-11T20:00:52Z","abstract_excerpt":"We study the behavior near the origin in $\\mathbb{R}^n ,n\\geq3$, of nonnegative functions \\begin{equation}\\label{0.1}\n  u\\in C^2 (\\mathbb{R}^n \\backslash \\{0\\})\\cap L^\\lambda (\\mathbb{R}^n ) \\end{equation} satisfying the Choquard-Pekar type inequalities \\begin{equation}\\label{0.2}\n  0\\leq-\\Delta u\\leq(|x|^{-\\alpha}*u^\\lambda )u^\\sigma \\quad\\text{ in }B_2 (0)\\backslash \\{0\\} \\end{equation} where $\\alpha\\in(0,n),\\lambda>0,$ and $\\sigma\\geq0$ are constants and $*$ is the convolution operation in $\\mathbb{R}^n$. We provide optimal conditions on $\\alpha,\\lambda$, and $\\sigma$ such that nonnegative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03778","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"}