{"paper":{"title":"Highly Oscillating Thin Obstacles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ki-Ahm Lee, Martin Str\\\"omqvist, Minha Yoo","submitted_at":"2012-04-16T12:31:55Z","abstract_excerpt":"The focus of this paper is on a thin obstacle problem where the obstacle is defined on the intersection between a hyper-plane $\\Gamma$ in $\\mathbb{R}^n$ and a periodic perforation $\\mathcal{T}_\\varepsilon$ of $\\mathbb{R}^n$, depending on a small parameter $\\varepsilon>0$. As $\\varepsilon\\to 0$, it is crucial to estimate the frequency of intersections and to determine this number locally. This is done using strong tools from uniform distribution. By employing classical estimates for the discrepancy of sequences of type $\\{k\\alpha\\}_{k=1}^\\infty$, $\\alpha\\in\\R$, we are able to extract rather pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3462","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"}