{"paper":{"title":"The Dirichlet problem in a planar domain with two moderately close holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Dalla Riva, P. Musolino","submitted_at":"2017-05-05T09:19:48Z","abstract_excerpt":"We investigate a Dirichlet problem for the Laplace equation in a domain of $\\mathbb{R}^2$ with two small close holes. The domain is obtained by making in a bounded open set two perforations at distance $|\\epsilon_1|$ one from the other and each one of size $|\\epsilon_1\\epsilon_2|$. In such a domain, we introduce a Dirichlet problem and we denote by $u_{\\epsilon_1,\\epsilon_2}$ its solution. We show that the dependence of $u_{\\epsilon_1,\\epsilon_2}$ upon $(\\epsilon_1,\\epsilon_2)$ can be described in terms of real analytic maps of the pair $(\\epsilon_1,\\epsilon_2)$ defined in an open neighborhood"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02142","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"}