{"paper":{"title":"Existence and dynamic properties of a parabolic nonlocal MEMS equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui","submitted_at":"2008-09-24T15:05:30Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^n$ be a $C^2$ bounded domain and $\\chi>0$ be a constant. We will prove the existence of constants $\\lambda_N\\ge\\lambda_N^{\\ast}\\ge\\lambda^{\\ast}(1+\\chi\\int_{\\Omega}\\frac{dx}{1-w_{\\ast}})^2$ for the nonlocal MEMS equation $-\\Delta v=\\lam/(1-v)^2(1+\\chi\\int_{\\Omega}1/(1-v)dx)^2$ in $\\Omega$, $v=0$ on $\\1\\Omega$, such that a solution exists for any $0\\le\\lambda<\\lambda_N^{\\ast}$ and no solution exists for any $\\lambda>\\lambda_N$ where $\\lambda^{\\ast}$ is the pull-in voltage and $w_{\\ast}$ is the limit of the minimal solution of $-\\Delta v=\\lam/(1-v)^2$ in $\\Omega$ wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4209","kind":"arxiv","version":3},"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"}