{"paper":{"title":"A note on the Trace Theorem for domains which are locally subgraph of a Holder continuous function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boris Muha","submitted_at":"2013-11-13T22:46:27Z","abstract_excerpt":"The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a H\\\" older continuous function. More precisely, let $\\eta\\in C^{0,\\alpha}(\\omega)$, $0<\\alpha<1$ and let $\\Omega_{\\eta}$ be a domain which is locally subgraph of a function $\\eta$. We prove that mapping $\\gamma_{\\eta}:u\\mapsto u({\\bf x},\\eta({\\bf x}))$ can be extended by continuity to a linear, continuous mapping from $H^1(\\Omega_{\\eta})$ to $H^s(\\omega)$, $s<\\alpha/2$. This study is motivated by analysis of fluid-structure interaction problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3329","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"}