{"paper":{"title":"Asymptotic profile of positive solutions of Lane-Emden problems 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":"2016-07-19T17:01:02Z","abstract_excerpt":"We consider families $u_p$ of solutions to the problem \\begin{equation}\\label{problemAbstract} \\left\\{\\begin{array}{lr}-\\Delta u= u^p & \\mbox{ in }\\Omega\\\\ u>0 & \\mbox{ in }\\Omega\\\\ u=0 & \\mbox{ on }\\partial \\Omega \\end{array}\\right.\\tag{$\\mathcal E_p$} \\end{equation} where $p>1$ and $\\Omega$ is a smooth bounded domain of $\\mathbb R^2$. We give a complete description of the asymptotic behavior of $u_p$ as $p\\rightarrow +\\infty$, under the condition \\[p\\int_{\\Omega} |\\nabla u_p|^2\\,dx\\rightarrow \\beta\\in\\mathbb R\\qquad\\mbox{ as $p\\rightarrow +\\infty$}.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05659","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"}