{"paper":{"title":"On vibrating thin membranes with mass concentrated near the boundary: an asymptotic analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luigi Provenzano, Matteo Dalla Riva","submitted_at":"2017-05-05T12:01:02Z","abstract_excerpt":"We consider the spectral problem \\begin{equation*} \\left\\{\\begin{array}{ll} -\\Delta u_{\\varepsilon}=\\lambda(\\varepsilon)\\rho_{\\varepsilon}u_{\\varepsilon} & {\\rm in}\\ \\Omega\\\\ \\frac{\\partial u_{\\varepsilon}}{\\partial\\nu}=0 & {\\rm on}\\ \\partial\\Omega \\end{array}\\right. \\end{equation*} in a smooth bounded domain $\\Omega$ of $\\mathbb R^2$. The factor $\\rho_{\\varepsilon}$ which appears in the first equation plays the role of a mass density and it is equal to a constant of order $\\varepsilon^{-1}$ in an $\\varepsilon$-neighborhood of the boundary and to a constant of order $\\varepsilon$ in the rest o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02181","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"}