{"paper":{"title":"The Moser-Trudinger inequality and its extremals on a disk via energy estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriele Mancini, Luca Martinazzi","submitted_at":"2016-08-25T14:25:49Z","abstract_excerpt":"We study the Dirichlet energy of non-negative radially symmetric critical points $u_\\mu$ of the Moser-Trudinger inequality on the unit disc in $\\mathbb{R}^2$, and prove that it expands as $$4\\pi+\\frac{4\\pi}{\\mu^{4}}+o(\\mu^{-4})\\le \\int_{B_1}|\\nabla u_\\mu|^2dx\\le 4\\pi+\\frac{6\\pi}{\\mu^{4}}+o(\\mu^{-4}),\\quad \\text{as }\\mu\\to\\infty,$$ where $\\mu=u_\\mu(0)$ is the maximum of $u_\\mu$. As a consequence, we obtain a new proof of the Moser-Trudinger inequality, of the Carleson-Chang result about the existence of extremals, and of the Struwe and Lamm-Robert-Struwe multiplicity result in the supercritical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07169","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"}