{"paper":{"title":"Estimates for capacity and discrepancy of convex surfaces in sieve-like domains with an application to homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram L. Karakhanyan, Martin Str\\\"omqvist","submitted_at":"2015-05-08T18:35:20Z","abstract_excerpt":"We consider the intersection of a convex surface $\\Ga$ with a periodic perforation of $\\R^d$, which looks like a sieve, given by $T_\\e = \\bigcup_{k\\in \\Z^d}\\{\\e k+a_\\e T\\}$ where $T$ is a given compact set and $a_\\e\\ll \\e$ is the size of the perforation in the $\\e$-cell $(0, \\e)^d\\subset \\R^d$. When $\\e$ tends to zero we establish uniform estimates for $p$-capacity $1<p<d$ and discrepancy of distributions of intersection $\\Ga\\cap T_\\e$. As an application one gets that the thin obstacle problem with the obstacle defined on the intersection of $\\Ga$ and perforations, in given bounded domain, is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02126","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"}