{"paper":{"title":"Pointwise Bounds and Blow-up for Nonlinear Polyharmonic Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Steven D. Taliaferro","submitted_at":"2015-05-01T19:25:36Z","abstract_excerpt":"We obtain results for the following question where $m\\ge 1$ and $n\\ge 2$ are integers.\n  Question. For which continuous functions $f\\colon [0,\\infty)\\to [0,\\infty)$ does there exist a continuous function $\\varphi\\colon (0,1)\\to (0,\\infty)$ such that every $C^{2m}$ nonnegative solution $u(x)$ of\n  $ 0 \\le -\\Delta^m u\\le f(u)\\quad$ in $B_2(0)\\setminus\\{0\\}\\subset {\\bf R}^n $\n  satisfies\n  $u(x) = O(\\varphi(|x|))\\quad \\text{as } x\\to 0 $\n  and what is the optimal such $\\varphi$ when one exists?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00254","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"}