{"paper":{"title":"Pointwise Bounds and Blow-up for Systems of Semilinear Elliptic Inequalities at an Isolated Singularity via Nonlinear Potential Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Igor E. Verbitsky, Marius Ghergu, Steven D. Taliaferro","submitted_at":"2014-02-01T19:11:00Z","abstract_excerpt":"We study the behavior near the origin of $C^2$ positive solutions $u(x)$ and $v(x)$ of the system\n  $0\\leq -\\Delta u\\leq f(v)$\n  $0\\leq -\\Delta v\\leq g(u)$ in $B_1(0)\\backslash\\{0\\}$ where $f,g:(0,\\infty)\\to (0,\\infty)$ are continuous functions. We provide optimal conditions on $f$ and $g$ at $\\infty$ such that solutions of this system satisfy pointwise bounds near the origin. In dimension $n=2$ we show that this property holds if $\\log^+ f$ or $\\log^+g$ grow at most linearly at infinity. In dimension $n\\geq 3$ and under the assumption $f(t)=O(t^\\lambda)$, $g(t)=O(t^\\sigma)$ as $t\\to \\infty$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0113","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"}