{"paper":{"title":"Overdetermined elliptic problems in nontrivial exterior domains of the hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Guowei Dai, Pieralberto Sicbaldi, Yong Zhang","submitted_at":"2024-05-07T14:26:05Z","abstract_excerpt":"We construct nontrivial unbounded domains $\\Omega$ in the hyperbolic space $\\mathbb{H}^N$, $N \\in \\{2,3,4\\}$, bifurcating from the complement of a ball, such that the overdetermined elliptic problem \\begin{equation} -\\Delta_{\\mathbb{H}^N} u+u-u^p=0\\,\\, \\text{in}\\,\\,\\Omega, \\,\\, u=0,\\,\\,\\partial_\\nu u=\\text{const}\\,\\,\\text{on}\\,\\,\\partial\\Omega\\nonumber \\end{equation} has a positive bounded solution in $C^{2,\\alpha}\\left(\\Omega\\right) \\cap H^1\\left(\\Omega\\right)$. We also give a condition under which this construction holds for larger dimensions $N$. This is linked to the Berestycki-Caffarelli-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04348","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.04348/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}