{"paper":{"title":"Critical points of the Moser-Trudinger functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Andrea Malchiodi, Francesca De Marchis, Luca Martinazzi","submitted_at":"2011-08-29T14:38:53Z","abstract_excerpt":"On a smooth bounded 2-dimensional domain $\\Omega$ we study the heat flow $u_t=\\Delta u +\\lambda (t)ue^{u^2}$ ($\\lambda(t)$ is such that $d/dt ||u(t,\\cdot)||_{H^1_0}=0$) introduced by T. Lamm, F. Robert and M. Struwe to investigate the Moser-Trudinger functional $E(v)=\\int_{\\Omega} (e^{v^2}-1)dx, v\\in H^1_0(\\Omega).$ We prove that if $u$ blows-up as $t\\to\\infty$ and if $E(u(t,\\cdot))$ remains bounded, then for a sequence $t_k\\to\\infty$ we have $u(t_k,\\cdot)\\rightharpoonup 0$ in $H^1_0$ and $\\|u(t_k,\\cdot)\\|_{H^1_0}^2\\to 4\\pi L$ for an integer $L\\ge 1$.\n  We couple these results with a topologic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5576","kind":"arxiv","version":2},"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"}