{"paper":{"title":"Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Hyder, Luca Martinazzi, Stefano Iula","submitted_at":"2016-10-21T15:17:55Z","abstract_excerpt":"Let $m\\ge 2$ be an integer. For any open domain $\\Omega\\subset\\mathbb{R}^{2m}$, non-positive function $\\varphi\\in C^\\infty(\\Omega)$ such that $\\Delta^m \\varphi\\equiv 0$, and bounded sequence $(V_k)\\subset L^\\infty(\\Omega)$ we prove the existence of a sequence of functions $(u_k)\\subset C^{2m-1}(\\Omega)$ solving the Liouville equation of order $2m$ $$(-\\Delta)^m u_k = V_ke^{2mu_k}\\quad \\text{in }\\Omega, \\quad \\limsup_{k\\to\\infty} \\int_\\Omega e^{2mu_k}dx<\\infty,$$ and blowing up exactly on the set $S_{\\varphi}:=\\{x\\in \\Omega:\\varphi(x)=0\\}$, i.e. $$\\lim_{k\\to\\infty} u_k(x)=+\\infty \\text{ for }x\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06820","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"}