{"paper":{"title":"A functional analytic approach for a singularly perturbed Dirichlet problem for the Laplace operator in a periodically perforated domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paolo Musolino","submitted_at":"2013-07-11T09:12:26Z","abstract_excerpt":"We consider a sufficiently regular bounded open connected subset $\\Omega$ of $\\mathbb{R}^n$ such that $0 \\in \\Omega$ and such that $\\mathbb{R}^n \\setminus \\cl\\Omega$ is connected. Then we choose a point $w \\in ]0,1[^n$. If $\\epsilon$ is a small positive real number, then we define the periodically perforated domain $T(\\epsilon) \\equiv \\mathbb{R}^n\\setminus \\cup_{z \\in \\mathbb{Z}^n}\\cl(w+\\epsilon \\Omega +z)$. For each small positive $\\epsilon$, we introduce a particular Dirichlet problem for the Laplace operator in the set $T(\\epsilon)$. More precisely, we consider a Dirichlet condition on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3023","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"}