{"paper":{"title":"Real analytic families of harmonic functions in a domain with a small hole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Matteo Dalla Riva, Paolo Musolino","submitted_at":"2013-06-26T09:41:48Z","abstract_excerpt":"Let n\\ge 3. Let \\Omega^i and \\Omega^o be open bounded connected subsets of R^n containing the origin. Let \\epsilon_0>0 be such that \\Omega^o contains the closure of \\epsilon\\Omega^i for all \\epsilon\\in]-\\epsilon_0,\\epsilon_0[. Then, for a fixed \\epsilon\\in]-\\epsilon_0,\\epsilon_0[\\{0} we consider a Dirichlet problem for the Laplace operator in the perforated domain \\Omega^o\\\\epsilon\\Omega^i. We denote by u_\\epsilon the corresponding solution. If p\\in\\Omega^o and p\\neq 0, then we know that under suitable regularity assumptions there exist \\epsilon_p>0 and a real analytic operator U_p from ]-\\eps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6185","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"}