{"paper":{"title":"A singularly perturbed Dirichlet problem for the Poisson equation in a periodically perforated domain. A functional analytic approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paolo Musolino","submitted_at":"2013-07-05T13:35:50Z","abstract_excerpt":"Let $\\Omega$ be a sufficiently regular bounded open connected subset of $\\mathbb{R}^n$ such that $0 \\in \\Omega$ and that $\\mathbb{R}^n \\setminus \\mathrm{cl}\\Omega$ is connected. Then we take $(q_{11},\\dots, q_{nn})\\in ]0,+\\infty[^n$ and $p \\in Q\\equiv \\prod_{j=1}^{n}]0,q_{jj}[$. If $\\epsilon$ is a small positive number, then we define the periodically perforated domain $\\mathbb{S}[\\Omega_{p,\\epsilon}]^{-} \\equiv \\mathbb{R}^n\\setminus \\cup_{z \\in \\mathbb{Z}^n}\\mathrm{cl}\\bigl(p+\\epsilon \\Omega +\\sum_{j=1}^n (q_{jj}z_j)e_j\\bigr)$, where $\\{e_1,\\dots,e_n\\}$ is the canonical basis of $\\mathbb{R}^n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1612","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"}