{"paper":{"title":"The Neumann problem in thin domains with very highly oscillatory boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e M. Arrieta, Marcone C. Pereira","submitted_at":"2011-04-01T04:30:09Z","abstract_excerpt":"In this paper we analyze the behavior of solutions of the Neumann problem posed in a thin domain of the type $R^\\epsilon = \\{(x_1,x_2) \\in \\R^2 \\; | \\; x_1 \\in (0,1), \\, - \\, \\epsilon \\, b(x_1) < x_2 < \\epsilon \\, G(x_1, x_1/\\epsilon^\\alpha) \\}$ with $\\alpha>1$ and $\\epsilon > 0$, defined by smooth functions $b(x)$ and $G(x,y)$, where the function $G$ is supposed to be $l(x)$-periodic in the second variable $y$. The condition $\\alpha > 1$ implies that the upper boundary of this thin domain presents a very high oscillatory behavior. Indeed, we have that the order of its oscillations is larger t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0076","kind":"arxiv","version":2},"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"}