{"paper":{"title":"A mixed problem for the Laplace operator in a domain with moderately close holes","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":"2019-03-14T08:43:54Z","abstract_excerpt":"We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter $\\epsilon$ and we define a perforated domain $\\Omega_{\\epsilon}$ obtained by making two small perforations in an open set. Both the size and the distance of the cavities tend to $0$ as $\\epsilon \\to 0$. For $\\epsilon$ small, we denote by $u_{\\epsilon}$ the solution of a mixed problem for the Laplace equation in $\\Omega_{\\epsilon}$. We describe what happens to $u_{\\epsilon}$ as $\\epsilon \\to 0$ in terms of real analytic maps and we compute an asymptotic e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05856","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"}