{"paper":{"title":"Isolated Singularities of Polyharmonic Operator in Even Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abhishek Sarkar, Dhanya Rajendran","submitted_at":"2015-01-08T10:43:40Z","abstract_excerpt":"We consider the equation $\\Delta^2 u=g(x,u) \\geq 0$ in the sense of distribution in $\\Omega'=\\Omega\\setminus \\{0\\} $ where $u$ and $ -\\Delta u\\geq 0.$ Then it is known that $u$ solves $\\Delta^2 u=g(x,u)+\\alpha \\delta_0-\\beta \\Delta \\delta_0,$ for some non-negative constants $\\alpha$ and $ \\beta.$ In this paper we study the existence of singular solutions to $\\Delta^2 u= a(x) f(u)+\\alpha \\delta_0-\\beta \\Delta \\delta_0$ in a domain $\\Omega\\subset \\mathbb{R}^4,$ $ a$ is a non-negative measurable function in some Lebesgue space. If $\\Delta^2 u=a(x)f(u)$ in $\\Omega',$ then we find the growth of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01793","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"}