{"paper":{"title":"Glueing a peak to a non-zero limiting profile for a critical Moser-Trudinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriele Mancini, Pierre-Damien Thizy","submitted_at":"2018-07-26T12:49:28Z","abstract_excerpt":"Druet [6] proved that if $(f_\\gamma)_\\gamma$ is a sequence of Moser-Trudinger type nonlinearities with critical growth, and if $(u_\\gamma)_\\gamma$ solves $$ \\begin{cases} &\\Delta u =f_\\gamma(x,u)\\,,~~ u>0\\text{ in }\\Omega\\,,\\\\ &u =0\\text{ on }\\partial\\Omega\\,, \\end{cases} $$ and converges weakly in $H^1_0$ to some $u_\\infty$, then the Dirichlet energy is quantified, namely there exists an integer $N\\ge 0$ such that the energy of $u_\\gamma$ converges to $4\\pi N$ plus the Dirichlet energy of $u_\\infty$. As a crucial step to get the general existence results of [7], it was more recently proved in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10098","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"}