{"paper":{"title":"Multiple blow-up solutions for the Liouville equation with singular data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Teresa D'Aprile","submitted_at":"2012-10-23T15:36:58Z","abstract_excerpt":"We study the existence of solutions with multiple concentration to the following boundary value problem $$-\\Delta u=\\e^2 e^u-4\\pi \\sum_{p\\in Z}\\alpha_p \\delta_{p}\\;\\hbox{in} \\Omega,\\quad u=0 \\;\\hbox{on}\\partial \\Omega,$$ where $\\Omega$ is a smooth and bounded domain in $\\R^2$, $\\alpha_{p}$'s are positive numbers, $Z\\subset \\Omega$ is a finite set, $\\delta_p$ defines the Dirac mass at $p$, and $\\e>0$ is a small parameter. In particular we extend the result of Del-Pino-Kowalczyk-Musso (\\cite{delkomu}) to the case of several singular sources. More precisely we prove that, under suitable restricti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6270","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"}