{"paper":{"title":"The Eigenvalue Problem for the $\\infty$-Bilaplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enea Parini, Nikos Katzourakis","submitted_at":"2017-03-10T12:18:19Z","abstract_excerpt":"We consider the problem of finding and describing minimisers of the Rayleigh quotient \\[ \\Lambda_\\infty \\, :=\\, \\inf_{u\\in \\mathcal{W}^{2,\\infty}(\\Omega)\\setminus\\{0\\} }\\frac{\\|\\Delta u\\|_{L^\\infty(\\Omega)}}{\\|u\\|_{L^\\infty(\\Omega)}}, \\] where $\\Omega \\subseteq \\mathbb{R}^n$ is a bounded $C^{1,1}$ domain and $\\mathcal{W}^{2,\\infty}(\\Omega)$ is a class of weakly twice differentiable functions satisfying either $u=0$ or $u=|\\mathrm{D} u|=0$ on $\\partial \\Omega$. Our first main result, obtained through approximation by $L^p$-problems as $p\\to \\infty$, is the existence of a minimiser $u_\\infty \\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03648","kind":"arxiv","version":4},"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"}