{"paper":{"title":"The critical dimension for a 4th order problem with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amir Moradifam, Craig Cowan, Nassif Ghoussoub, Pierpaolo Esposito","submitted_at":"2009-04-15T23:27:01Z","abstract_excerpt":"We study the regularity of the extremal solution of the semilinear biharmonic equation $\\bi u=\\f{\\lambda}{(1-u)^2}$, which models a simple Micro-Electromechanical System (MEMS) device on a ball $B\\subset\\IR^N$, under Dirichlet boundary conditions $u=\\partial_\\nu u=0$ on $\\partial B$. We complete here the results of F.H. Lin and Y.S. Yang \\cite{LY} regarding the identification of a \"pull-in voltage\" $\\la^*>0$ such that a stable classical solution $u_\\la$ with $0<u_\\la<1$ exists for $\\la\\in (0,\\la^*)$, while there is none of any kind when $\\la>\\la^*$. Our main result asserts that the extremal so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2414","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"}