{"paper":{"title":"Asymptotic analysis for the Lane-Emden problem in dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, Francesca De Marchis, Isabella Ianni","submitted_at":"2016-02-22T20:12:21Z","abstract_excerpt":"We consider the Lane-Emden Dirichlet problem \\begin{equation}\\tag{1} \\left\\{\\begin{array}{lr}-\\Delta u= |u|^{p-1}u\\qquad \\mbox{ in }\\Omega u=0\\qquad\\qquad\\qquad\\mbox{ on }\\partial \\Omega \\end{array}\\right. \\end{equation} when $p>1$ and $\\Omega\\subset\\mathbb R^2$ is a smooth bounded domain. The aim of the paper is to survey some recent results on the asymptotic behavior of solutions of (1) as the exponent $p\\rightarrow \\infty $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06919","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"}