{"paper":{"title":"A gap for eigenvalues of a clamped plate problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Daguang Chen, Guoxin Wei, Qing-Ming Cheng","submitted_at":"2016-10-19T07:14:35Z","abstract_excerpt":"This paper studies eigenvalues of the clamped plate problem on a bounded domain in an $n$-dimensional Euclidean space. We give an estimate for the gap between $\\sqrt {\\Gamma_{k+1}-\\Gamma_{1}}$ and $\\sqrt {\\Gamma_{k}-\\Gamma_{1}}$, for any positive integer $k$. According to the asymptotic formula of Agmon and Pleijel, we know, the gap between $\\sqrt {\\Gamma_{k+1}-\\Gamma_{1}}$ and $\\sqrt {\\Gamma_{k}-\\Gamma_{1}}$ is bounded by a term with a lower order $k^{\\frac1n}$ in the sense of the asymptotic formula of Agmon and Peijel, where $\\Gamma_j$ denotes the $j^{^{\\text{th}}}$ eigenvalue of the clamped"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05889","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"}